In the absence of anything resembling a competitive match on his way into the third round, Novak Djokovic turned his attention on Thursday to a tougher examination of his resolve: the provocative suggestion by John McEnroe that the Serb’s off-court problems over the past year resemble those of the deeply troubled Tiger Woods.

After dismissing the frankly embarrassing challenge of the 22-year-old Czech Adam Pavlasek in a little over an hour and a half on No1 Court, 6-2, 6-2, 6-1, Djokovic came smiling and innocent into a minor blizzard of questioning. He was toweringly diplomatic, brilliantly evasive and, in the end, a little po-faced.

“I have heard about it today,” he said of the McEnroe headlines that had picked up on his indiscretions from the BBC the day before. “Look, John has a complete right to say … anybody, really, in the world has a right to say what they want, and I respect that right – especially coming from John, because he’s someone that has earned that right because of who he is and what he has meant to the sport and what he still is representing as a former player and still being very active on the tour.”

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But what about the inference that Djokovic’s life was in a comparable meltdown – especially with the image of Woods being interrogated by police recently in a state of advanced disrepair? “He’s very well known for his, you know, kind of bold comments,” the Serb said of McEnroe, “and not really caring too much about being politically correct, but saying whatever is on his mind. I really don’t take anything personal. I always got along very well with John. I guess whether that’s his opinion or criticism or something else, I’m not really sure. But in the end of the day, I respect everything he says.”

There were, at this point, a good many feet shuffling and eyebrows tilting upwards, at least among the cynical wing. Was there, one inquisitor wondered, any truth in what McEnroe said?

“I’m not sure. I always got along very, very well with John. We even practised a few years ago before one of my matches in US Open, and [he] was always talking nicely about me. I really don’t take it in a negative way anyhow. It’s fine. He has his right to say the things he wants to say. I don’t necessarily need to agree with that. But it’s his right. I don’t know where was the basis, and he was just maybe making a comparison. I’m not really sure.”

He added: “When I was warming up for my first match on the Centre Court, he was giving an intro, talking to the camera, and I served and the serve went straight at him as I was playing. I don’t know. Maybe it’s because of that. Maybe he thought it wasn’t a joke, and I was joking, [that] I was trying to hit him. I don’t think there was any kind of really wrong intention from his side towards me.”

As for the tennis, it is likely, although not certain, that Djokovic will get a better argument out of Ernests Gulbis on Saturday than he did during his mobile sunbathing in the company of Pavlasek on Thursday.

If Andre Agassi had asked his Serb charge to go out and get a hitting partner to keep him sharp for the third round, he could not have chosen more wisely. Pavlasek – who beat the American Ernesto Escobedo in four sets on Tuesday, his only Tour-level success all year – was once a promising junior but has caused barely a ripple in his time on the Tour.

This was blindingly apparent not only from his ranking (he reached a career high of 72 in January, and has since crashed like the stock market) but also his seeming willingness to put the ball in the path of his childhood idol at every opportunity.

After the farce of Martin Klizan’s withdrawal against Djokovic in the first round, Pavlasek did little to influence the scoreline either, except provide the smaller numbers. A time violation at 2-1, a deuce in the third set and a taunt by a wise guy in the Czech’s box troubled Djokovic more.

Gulbis, meanwhile, caught Juan Martín del Potro off guard to win 6-4, 6-4, 7-6 (3) on court No3. That was a surprise rather than a full-blown shock because Del Potro has struggled with injuries for so long, and Gulbis is invariably a few shots away from doing amazing things on a tennis court, or their polar opposite.

The Latvian is also up there in the crazy-dude stakes with Fabio Fognini and Alexander Bublik, a gifted entertainer with the day-time focus of a barn owl. He has beaten Djokovic once in seven attempts, eight years ago in Brisbane, and lost to him in their only previous grand slam contests, on the clay of Roland Garros.

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Gulbis, whose star briefly shone as brightly as any, plainly was overjoyed. “It’s very satisfying,” he said. “I found out yesterday that it was my first win in 13 months in a Tour level main draw. I won one challenger match and I won one qualie match in Rotterdam. I played well my first-round match. This match I played really, really great tennis. I served well, I returned well. In my opinion, Del Potro is one of the best players.”

Del Potro said: “He’s a very dangerous opponent to play on grass, and he did much better than me today. I know how good is Ernests on grass and if he has a good day he can beat all the guys, because he already made it in the past.”

The challenge for Djokovic now is three-fold: combating the eccentricities of Gulbis, the loosest cannon in the business, fighting off complacency after his two easiest matches of the year and not listening to McEnroe.

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While Djokovic continues his search for serenity, Roger Federer appears to permanently reside in that happy state, although he did have some grief in the first set before seeing off the lesser Serb, the world No79, Dusan Lajovic, 7-6 (0), 6-3, 6-2, serving it out to love with a second-serve ace, his ninth, at 122mph down the T, on a darkening Centre Court after an hour and a half.

With dark clouds already looming Federer had looked to be in a hurry to get the job done and broke early in the second set to assume complete control. “I’m happy to come through the second round,” he said.

“I couldn’t get rid of the nerves early on and struggled to find my rhythm. I got back in and broke him back but struggled throughout the first set. In the end it was very good.

“My parents were delighted to be invited to the royal box, along with Tim Henman’s parents. And I was happy to win in front of them.”

On Saturday, Federer plays Mischa Zverev, the German serve-and-volleyer who took five sets to get rid of Mikhail Kukushkin – but he will have one eye on Djokovic’s progress all the way to the semi-finals – presuming they both get there.