The Serbian top seed didn't even seem to notice the wind swirling in Arthur Ashe Stadium, firing 13 aces and 33 total winners past the Frenchman.
But he was pleased to get his day's work done with even more efficiency than he showed in a straight-sets first-round win over Argentina's Diego Schwartzman.
"I don't feel like I need to play long matches to get into the groove," Djokovic said. "I came up with a very good performance. Stayed mentally tough and didn't allow myself to get frustrated because of the wind and conditions that were obviously very tough for both of us."
In fact, Djokovic looked more uncomfortable being asked post-match to demonstrate some dance steps for the crowd than he did facing anything that Mathieu threw at him.
The brisk performance helped dispel any lingering suggestion that marriage and impending fatherhood had distracted Djokovic from the game, and perhaps left him vulnerable.
Djokovic himself unwittingly reinforced that idea with a pre-match remark that with a baby coming, tennis was not his number one priority.
The Wimbledon champion said Thursday that didn't mean he was taking a chance at an eighth Grand Slam title lightly.
"I think there is no question about it, my full priorities and commitments and energy goes to my family as much as I need to, but that doesn't mean that I'm 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."
And Djokovic, whose four trips to the final in the past four years yielded one title in 2011, was relishing the prospect of a third-round meeting with American Sam Querrey, hoping for a marquee night match to stir up the New York crowd.
Querrey, one of just three US men to make it into the second round, advanced with a 6-3, 6-4, 6-4 win over 28th-seeded Spaniard Guillermo Garcia-Lopez.
"Sam is playing in front of his crowd, I'm sure that he's going to have some good support," Djokovic said. "But on the other hand, if we get to play on center court maybe night session, that's where my experience kicks in, I think.
"I have had a lot of matches, night sessions," he added. "I'll try to neutralize his serve that is his big weapon. If he serves well he's very dangerous."