* American Querrey next opponent for Djokovic
* Winning still a priority for the Serb (Adds quotes, detail, byline)
NEW YORK, Aug 28 (Reuters) - World number one Novak Djokovic barely worked up a good sweat on another sizzling day at the U.S. 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 on Thursday.
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 U.S. 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," said Djokovic. "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," said Djokovic. "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." (Editing by Frank Pingue/Mark Lamport-Stokes)