World number one Novak Djokovic barely worked up a good sweat on another sizzling day at the US Open as he strolled past Paul-Henri Mathieu 6-1 6-3 6-0 and into the third round of the year’s final Grand Slam.

Djokovic, who has reached the Flushing Meadows final each of the last four years and won it all in 2011, needed just 88 minutes to dismiss the veteran Frenchman on a gusty Arthur Ashe Stadium court.

The Wimbledon champion broke Mathieu to open the match and never eased off the gas as he swept through the last seven games to clinch an emphatic win. “I have nothing to complain about, I wanted to get my job done as quick as possible,” said Djokovic.

“I don’t feel like I need to play long matches to get into the groove. “I mean, I feel that I’m hitting the ball very well. Second match even better than the first one.

“Under the circumstances I think I came up with a very good performance. Stayed mentally tough and did not allow myself to get frustrated because of the wind and conditions that were obviously very tough for both of us.”

It has been a smooth start to US Open for Djokovic, who opened his campaign with an equally dominant display as he eased past Argentine Diego Schwartzman in straight sets.

But things should get tougher in the third round where the Serb will run into big-hitting American Sam Querrey, who advanced with a 6-3 6-4 6-4 win over 28th seed Guillermo Garcia-Lopez of Spain. "It's logical to expect that every next match that you play in a grand slam will get tougher," he said.

“Sam is playing in front of his crowd. I’m sure that he’s going to have some good support.

“But on the other hand, if we get to play on centre court, maybe night session, that’s where my experience kicks in, I think. “I have had a lot of matches, night sessions if we get to play, as I said, and (I will) try to neutralise his serve that is his big weapon. If he serves well, he’s very dangerous.”

Djokovic, who had won only two matches in the hard court run-up to Flushing Meadows after getting married just days after his Wimbledon triumph, has looked like his old dominating self. Playing his first grand slam as a married man,

Djokovic, who is also about to become a first-time father, had talked about a shift in priorities but underscored that he is still fully focused on the task at hand when he steps onto the court.

“My focus is there. I don’t understand how the people really got what I said, but I don’t think there is anything wrong.

“Actually, I think it would be much (more) wrong if my tennis is in front of my baby and my wife.

“I think there is no question about it. My full priorities and commitments and energy go to my family as much as I need to, but that doesn’t mean that I’m not going to play tournaments or not going to continue on doing what I was doing so far.

“Of course I’m doing everything that I can, respecting the same daily routines that I had for many years with my team and it’s working well. I have big support from my wife, from my family, from my team. We are all on the same page.”

Meanwhile Andy Murray enjoyed a pleasingly drama-free evening as he eased into the third round.

After his struggles with cramp against Robin Haase on Monday that almost proved terminal to his hopes for the tournament, what was required against German qualifier Matthias Bachinger was a straightforward outing.

And that was exactly what played out under the lights on Arthur Ashe Stadium, Murray wrapping up a 6-3 6-3 6-4 win in an hour and 46 minutes to set up a meeting with Russian Andrey Kuznetsov tomorrow.

The eighth seed said: “The second and third sets was good tennis, we had some fun points. I moved well tonight. I struggled a lot in my first match but I pulled up okay.

“To play a night session, I love it. I came to watch the women’s final when I was 15 years old and sat right at the top. I always wanted to come back and play one myself.”

On paper this was a mismatch — a two-time grand slam champion against a man who is ranked 235th and only won his first grand slam match three days ago.

Perhaps that explained the sparse crowd, with Arthur Ashe Stadium looking particularly cavernous at less than a quarter full at the start.

But after Murray’s struggles this season and especially on Monday, nothing could be taken for granted.

It was cool and windy, which did not make for high-quality tennis in the opening stages. The last time the two 27-year-olds played each other was in the juniors 13 years ago before their careers took very different paths.

Bachinger did not look at all overawed by the occasion but a couple of loose shots in the eighth game cost him, giving Murray a break and the chance to serve for the set. He managed that with no alarms, serving an ace on his first set point.

Bachinger was the most unlikely player to make the second round, the German only finding out two days before his first qualifying match that he had been given a place.

He flew to New York from Munich the next day, defying jet lag to win three matches in three days and then beat Radek Stepanek in the first round proper.

He had not dropped more than three games in any set before this match but Murray represented a step up in class.

The Scot seemed to relax after winning the first set and began to show some of the variety he knows coach Amelie Mauresmo will encourage.

He was keen to come to the net, while a couple of exquisite lobs found their target when his opponent ventured forward.

Murray extended his winning run of games to five with a break at the start of the second set.

Bachinger was being dragged all around the court and was powerless to stop Murray taking the second set with another break after an hour and two minutes.

Murray had not faced a break point all match but, with the Scot serving into the wind, Bachinger took his chance to attack in the fifth game of the third set and suddenly it was 0-40.

Murray was not fazed, though, calmly saving all three before holding to put the pressure back on his opponent.

The moment looked to have arrived in the eighth game when three Bachinger errors made it 0-40, only for Murray to play three of his poorest points of the match.

Bachinger saved two more break points with big serves, much to Murray’s frustration, but he was not to be denied for long.

Three more chances arrived in the German’s next service game, and this time they were match points. Murray took the first, forcing Bachinger into a backhand error.