According to the ATP rankings, Dustin Brown is the world's 78th best tennis player. Yet just over a week ago, at the Gerry Weber Open – a Wimbledon warm-up event in Halle, Germany – he beat the world No 1, Rafael Nadal, in straight sets. Actually, beat is too polite a word; pulverised would be better. From 4-4 in the first set, Brown reeled off seven consecutive games, reducing Nadal to the unfamiliar role of bit-player. The Spaniard wasn't playing badly – he just couldn't lay his racket on the ball. Aces thundered past him. Service returns streaked to the corners. When Nadal did get the ball in, Brown, who is 6ft 5in and whose body seems to consist entirely of arms and legs (plus flailing dreadlocks), would bound to the net and finish off the point, often with an outrageous angled drop volley or a jubilant slam dunk. Seldom can Nadal have been so comprehensively outplayed, so spectacularly dusted up.

Not surprisingly, the crowd went wild. They were, after all, witnessing a home player pulling off a massive upset, the equivalent of, say, British No 2 Dan Evans taking out Novak Djokovic at Wimbledon. But the excitement was about more than this. It was also to do with the personality and playing style of Brown himself. Brown is a flamboyant presence in a sport that, in recent decades, has become increasingly uniform. He is professional tennis's closest thing to an eccentric. No one else looks like him. No one else has his repertoire of on-court antics (the celebratory leaps, the eight-foot-high racket tosses). And certainly no one else plays like him. The man who, on Twitter, styles himself as DreddyTennis plays the game in a totally unique way – and the result is utterly captivating to watch.

Halle is a small town in Westphalia, miles from anywhere. Its one claim to fame is that it is home to the headquarters of the Gerry Weber women's clothing empire – Germany's answer to Topshop. No effort is spared in reminding you of this. The tennis takes place at the Gerry Weber Stadium, located on the town's periphery. The stadium itself is part of the Gerry Weber Sportpark, a sprawling complex of halls and gyms that seems to take up almost as much territory as the town itself. Next to the Sportpark are two Gerry Weber hotels, one ultra-smart (where the players and their entourages stay), one more modest (reserved for grunt workers, journalists). There's only one way to get to the fancier of the two: you have to walk up Roger-Federer-Allee. (The Swiss player loves coming here and has won the tournament seven times, including this year, which is presumably why he has had a street – or, more accurately, a driveway – named after him.)

It's three days since Brown's victory over Nadal and he and I are sitting in the (smart) hotel lobby. He is out of the tournament, both singles and doubles, but doesn't seem too upset. For a player like him, ranked in high double figures, it has been a memorable, possibly life-changing, week. He reached the semi-finals of the doubles and, in the singles, made it to the quarters before going out, in unbelievably dramatic fashion, to Philipp Kohlschreiber, the German No 2. Brown really should have won – he squandered five match points – but, as is often the case, he couldn't sustain his brilliance for quite long enough. Serving for the match, he hit a succession of double faults. On one of his match points, he smashed a relatively easy forehand long. ("It's a shot I would make eight out of 10 in practice.") The match was settled by a truly nerve-shredding tie-break, which Kohlschreiber – to the disappointment of almost everyone in the crowd – won 18-16.

I ask Brown what it's like losing a match like that. Does he now regret not reining in his ultra-attacking style just a bit near the end? (For instance, the shot that handed Kohlschreiber his decisive match point was a reckless overhead backhand volley that flew into the net.) "It doesn't help to think that way," Brown replies. "Afterwards of course you're always smarter. But playing all-out attack is my game, it always has been, and if I hadn't been so aggressive I probably wouldn't have got to the point where I had the chance to win. It's easy to beat yourself up afterwards, but on any of those match points he could have missed a shot. That's just tennis. I'm not about to change the way I play."

In person, Brown is not quite as eccentric as he comes across on court. He speaks quickly and seriously, at times a note of prickliness entering his voice. He is both articulate and guarded. His appearance contrasts markedly with his verbal manner: he looks intensely – improbably – relaxed. He doesn't so much sit as spread himself out upon the sofa, his body inclining ever closer towards the horizontal the longer our conversation progresses. (It is, admittedly, a comfortable-looking sofa.) His attire is a blend of the sporty and the scruffy: bright orange Nike trainers, black tracksuit bottoms, a loose-fitting T-shirt emblazoned with Jamaican imagery, chunky headphones round his neck, dreads bunched up in a turquoise Rasta cap. Brown, one senses, is unfazed by the attention that is increasingly being paid to him. He is currently all over the German press. The day after his victory over Nadal, he was interviewed on national TV. During our interview, people keep coming up to congratulate him, asking him to pose for photos, wishing him luck at Wimbledon.

Brown's father is Jamaican, his mother German. (When he speaks in German, he sounds very German; when talking in English, a Caribbean lilt enters his voice.) His parents, Leroy and Inge, met in Jamaica before settling in Celle, a town close to Hanover and not all that far from Halle. Brown was born there in 1984. He describes his early childhood as being an endless round of sports practices: in addition to tennis, he played football, handball and judo. Aged eight, he realised that he had to make a choice and so decided to drop the other sports and concentrate on tennis. Could he really have been so sure about his future at such a young age? With a definiteness that perhaps reveals something about the single-mindedness required to be a tennis pro, Brown tells me that, from the start, he knew he wanted to get to –or near – the top. "When I made the decision to pursue tennis instead of soccer, of course I wanted to be successful. I didn't want just to end up playing for a club somewhere."

How was it, I ask, growing up in provincial Germany, looking as he did?

"Sure, I stood out. And there were a lot of problems when I was younger, both at school and in the tennis world. A lot of people don't talk about it for whatever reason, but racism was definitely around then, and still is now. Mostly, it's fine, I've got used to it, but even nowadays it can be a problem."

Shockingly, Brown tells me that he still gets turned away from bars or clubs near where he lives. "If you're with one guy it doesn't matter so much, you go somewhere else, but if there are six or seven of you, and none of them can get in because of one guy – and that guy always tends to be me – it kind of takes the fun out of the whole thing."

As a junior, Brown was talented, but not spectacularly successful – "I wasn't close to being the German No 1 for my age or anything like that." Nevertheless, he attracted the attention of Kim Wittenberg, an American who ran a tennis academy near Hanover, and soon he was going there regularly for coaching. ("It was Kim who taught me to play tennis.") An apprenticeship within the German tennis system beckoned, but when he was 11, Brown's parents decided to emigrate (or, in his father's case, return) to Jamaica. The move was largely dictated by finances. "My parents didn't have a lot of money. Tennis was very expensive in Germany – you had to pay light fees, hall costs, plus the coaching." But there may, Brown hints, have been other factors in the decision. "I was pretty mentally soft when I was young. Anything could happen when I played – I could lose my temper, I got disqualified." The move to Jamaica may partly have been conceived as a means to instil some much-needed discipline.

Certainly, things were very different in Jamaica – no tennis centres, hardly any tournaments. "I went to the local courts, became friends with the guys there, and basically just spent my time hitting balls with them. I didn't have a coach." (When Brown returns to Jamaica now, he still goes to the same courts: "Most of the guys I used to play with are still there. We'll hit a few balls, sit down and talk.")

Given the lack of infrastructure, the move to Jamaica could have had a negative impact on his development, but Brown insists that it was beneficial. "Things were just so different. Coming from Germany, having a Game Boy, cable TV and stuff and going to Jamaica and having to realise, 'Shit, there are other things in the world that are important.' I'm very thankful that happened. Maybe without going there I wouldn't be where I am right now. It was good for me to see another side of life, to realise that it wasn't all Germany."

When Brown was through playing juniors, he stayed on in Jamaica. At the time – the early 00s – the island hosted a series of Futures events, the lowest-level type of professional tournament. It therefore made sense for him to live there – where his costs were minimal – while competing on the Futures circuit. That's what he did for the next four years. However, he soon realised he was caught in a trap: by competing in just a few events, he wasn't earning enough money – or enough ranking points – to move up to the higher-grade tournaments that would allow him to make significant strides up the rankings. His future as a tennis player became precarious. In 2004, therefore, Brown's parents took a decision that, though unorthodox, ultimately enabled him to build a life for himself as a fully-fledged pro.

Dustin Brown celebrates after beating the world No 1 Rafael Nadal at Germany's Gerry Weber Open on 12 June. Photograph: Carmen Jaspersen/AFP/Getty Images

The family relocated to Germany, and his parents took out a loan to buy their son a VW camper van ("one of the large kinds with three beds and a separate bathroom"). The plan was simple: Brown would use the van to tour around Europe, thereby eliminating hotel and restaurant costs from his budget. "It was a brilliant idea by my parents, otherwise I wouldn't have been able to go on playing. It was a means of competing week in week out." For the next five years, Brown lived the life of a tennis nomad, pitching up in a new town each week, cooking pasta for himself in the evenings, hopefully winning enough prize money at each event to allow him to pay for the fuel to take him on to the next one.

How does he look back on that period now? "Of course, it was far from the ideal existence of a professional tennis player. It was a tough life but it was also a lot of fun." Brown found innovative ways to supplement his income. "I had my own stringing machine, and I'd stay up at night stringing rackets for other players. Tournament costs for stringing were maybe €10 a shot then, and I did them for €5. No one had much money, so everyone would come to me." Other players, he says, occasionally availed themselves of his van's spare beds. "Once in a while other guys didn't want to pay hotel costs so they'd stay with me and give me some money on the side."

What did his fellow professionals make of him? "At the start it was awkward, people didn't know who I was, everyone was like, 'Who's this guy with the camper?' But after a while, meeting people, playing better, playing doubles, stringing rackets for the guys, you get to know everyone. Call it hustling, grinding, whatever you want…we were all just trying to get on to the big tour."

Brown's first really big breakthrough came in 2009, when he made it through to the finals of several Challenger events. (Challengers are the next level up from Futures; they are the rung below the main ATP tour.) It was around this point, he says, that he could finally afford to ditch the camper. (It now resides, mostly unused, at his mother's house.) The following year, he broke the top 100 for the first time – the target he set himself when he started out as a professional – and began making both decent money and a name for himself. Exasperated with the lack of support he was getting from the Jamaican tennis federation, he also decided, around this point, to switch to playing as a German. (He already had dual citizenship, so this wasn't too hard.) Tennis, he says, is incredibly low down the pecking order in Jamaica. Even though he was by now the island's most successful player of all time, his results weren't even reported by the local papers.

In the four years since, Brown's career hasn't exactly gone stratospheric, but he has made solid progress. At Wimbledon last year, he put in a remarkable performance – replete with Boris Becker-style dives – to defeat former champion Lleyton Hewitt in the second round. Earlier this year, he won his first ever match against a top 10 player – John Isner – and his current ranking of 78th is a career high.

Yet for all his success and the growing excitement that surrounds him, Brown's existence remains precarious. The wealth and fame enjoyed by those at the top of the game still seem a long way off. Money continues to be a problem. In the past few years, Brown has reunited with his childhood coach, Kim Wittenberg, who now travels with him for part of the year. "I would love it if Kim could be with me all the time. Having him with me makes me play better. But I'm not at a point when I can afford that yet."

So far this year, for instance, Brown has earned $158,000 in prize money. He is also guaranteed a significant pay cheque by competing in the main draw at Wimbledon, which, as a top 100 player, he is guaranteed to do. (Even first-round losers take home £27,000.) Yet Brown points out that while his salary sounds more than healthy on paper, it isn't so impressive when the exorbitant costs of being a tennis player are taken into account. "You have to pay for everything: hotel bills, flights, food, laundry costs. I'd love to have a physio as well as a coach travelling with me, but there's no way I can afford it."

He still counts the pennies. Just recently, he says, he and a fellow pro spent three hours in a launderette, washing their kits. "The tournament we were playing in had a laundry service, but their prices were ridiculous – €1.50 for a sock, €3 for a pair of shorts!"

Tennis, of course, is sport whose earning structure contrasts sharply with that of, say, football, where even the 78th best player in Britain is probably a millionaire. What does he make of such inequalities? Does he envy the gilded existence of the likes of Andy Murray? Brown's reply is impressively grounded: "Of course I'd like to make more money. It would be nice to not have to work again when I finish playing. But the top guys are there for a reason. And things are going really well for me. It's hard to compare or say I would swap because I haven't been through the things that Andy Murray has been through and he hasn't been through the things I've been through. I'm pretty sure he's had a lot of difficulties with his injury recently. Everyone has to deal with their own problems and get through it. No one has a life where everything's perfect."

On the morning of his final day in Halle, Brown took part in an exhibition match against his doubles partner, Jan-Lennard Struff. The match was watched by a decent crowd: around a third of the stadium's 10,000 seats were occupied. Given the range of other attractions on offer (a staggering number of beer tents and wurst stands; a music stage), it was an impressive turnout, and testament to Brown's compelling style of tennis. From Halle, Brown travelled to Holland, where this week he's been competing in the Topshelf Open. (Because of his success at Halle, he was too late for the singles qualifiers and so could only play doubles.) Now he's in London, gearing up for Wimbledon, where, he says, it's his goal to make the second week (which means getting to the fourth round or better).

In the press conference after his match against Kohlschreiber, Brown was gung ho about his chances at Wimbledon. "I am playing well, grass is my favourite surface, I'm not afraid of anyone in the draw. It's the other players who are afraid of me, not the other way round." If he can recapture anything like the form he displayed at Halle, the rest of the tennis world should indeed be nervous.