They call the time trial the race of truth: the ultimate test of man and bike against the clock. And as Geraint Thomas slipped through the crowds of fans waving red, green and white flags – the colours of the Basque country as well as his native Wales – and surged towards the finish in Espelette he found what he had been looking for during these past three weeks. Yes, he was good enough to win the Tour de France. And by quite some distance too.

True, there were a few bumps on the 31km road from Saint-Pée-sur-Nivelle, especially when he nearly stacked his bike on the rain-slickened tarmac. But the 32-year-old Welshman was able to ease down over the final hill, content in a third-place finish on the stage behind Tom Dumoulin and Chris Froome, whose performance was good enough to move him up to third on general classification.

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Thomas now heads to Paris on Sunday with a 1min 51sec buffer over Dumoulin. And with tradition dictating that the yellow jersey is not attacked during the final stage, he will join Bradley Wiggins, who won the race in 2012, and Chris Froome, who triumphed in 2013, 2015, 2016 and 2017, on the roll call of British winners.

As the Welshman crossed the line, 14sec behind Dumoulin on the 20th stage, he pounded his chest and threw his hands in the air in disbelief. Then, after hugging his wife, Sara Elen, he poured water over his head as if to make sure this was not an impossible dream. Later he also threw his arms around the Team Sky principal, Dave Brailsford, and suddenly the tears began to flow.

"For three weeks it was always about the process, and staying focused day-by-day, and suddenly it was all over and I had done it and the world came falling down," admitted Thomas. "There was just huge emotion. I was welling up every time I hugged someone for 20 minutes.

"I felt I could beat the guys here, but to do it over three weeks is insane. The last time I cried was when I got married – I don’t know what has happened to me."

Facebook Twitter Pinterest Thomas celebrates on the podium. Photograph: Philippe Lopez/AFP/Getty Images

Thomas had looked pensive beforehand, puffing out his cheeks on the start line as if trying to also exhale the tension building up inside. He had won Olympic medals, Paris-Nice and the Dauphiné, but it was only in the last few days that he started to imagine being in this situation.

He was the last rider off the ramp at 4.30pm local time, the challenge of a punchy course with rolling roads and sharp climbs made steeper by the falling rain. Not that he appeared worried as he quickly increased his lead over Dumoulin on general classification in the first 10km of the stage.

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But then came near disaster as, after 12km, he wobbled and nearly stacked the bike. "I felt really good on the stage, actually," he said. "Really strong. But I was pushing a bit hard on the corners so the team told me to relax and make sure I won the Tour. At the start the course didn’t seem too technical, but at the end every corner seemed to be 180 degrees."

Wisely, then, he slowed down, knowing that victory was his. Minutes beforehand Dumoulin had been able to secure his first stage victory of the Tour as well as second place on the podium with a one-second time-trial win over Froome.

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What made the Dutchman’s performance more impressive was that he had lost his skinsuit – and had to have a new one delivered from San Sebastián just before the stage.

"It was a stressful morning for me and everyone," admitted Dumoulin. "I was utterly pissed. But I really have to thank our clothing sponsor big time. They called up a retired seamstress and they made up a new suit on Saturday morning and drove it here."

Behind him on the road a large crowd was cheering Thomas home, including dozens of delighted fans from Wales. Seeing such positivity has not always been the case for Team Sky on this Tour, with Thomas regularly booed on the podium by a French public sceptical of his team’s achievements.

It was only on Friday that a Team Sky car was pelted with eggs by fans. The French paper Le Monde warned that while it believed Thomas's lead was legitimate, the fans they had spoken to during the past three weeks had greater scepticism.

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"A Welsh track specialist who, at the age of 32, wins the Tour de France, is it a miracle? For the latter case, we would tend to answer no," the paper wrote. "And yet, nobody believes it: we spoke Tour de France every morning in the cafes of the departed cities. Among the French, we must create folders and subfolders. Those who watch the Tour; those who watch the race; those who believe in the regularity of the race they watch.

"In this last file, there is no one left. They respect, of course, the efforts and the sufferings, adhere to the myth of the convicts of the road. But the dice seem stuck."

Yet Thomas is widely liked by all the peloton – and by most fans, too. They admire the way he rode during the 2013 Tour de France with a fractured pelvis, which required him to be lifted into his saddle. He described it as "the worst pain I’ve ever experienced on a bike" – yet never took anything stronger than ibuprofen for the pain.

Eight years earlier he also needed an operation to remove his spleen, after a piece of metal flicked up from the road into the spokes of his front wheel, in Australia. Yet on Saturday evening all the struggles and strife were suddenly worth it.

Some doubters have pointed out that Thomas has never finished higher than 15th in a grand tour. That, however, must be placed into context, given the Welshman has usually ridden in support of other riders rather than as a general classification contender. Yet it was only on the final few moments of this Tour that he finally truly believed that he was capable of winning a yellow jersey.

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"I know people won’t believe it, but it was only on Friday night that I started to think about it," he said.

"That last mountain stage was just a fight and I knew I had to just follow Tom like poo on a shoe. On Saturday I won’t celebrate too much because if you switch off the Champs Élysées is hard. I’m going to have a burger and certainly a beer or two but I will save the real celebrations for Paris on Sunday night."

And then came the biggest and brightest of smiles. In the past, Thomas’s progress has also been interrupted by an unfortunate succession of bad days and even nastier crashes.

Not this time, though. He has ridden with maturity and class throughout this Tour. And he emerges as the most worthy of winners.