As good as Djokovic was from the start, Mathieu was his own worst enemy, serving seven double faults in the opening set as he struggled to adjust to the windy conditions.
The Frenchman settled down in the second set and had a chance to break for 3-2 but could only watch as his forehand clipped the top of the net and dropped just wide. Djokovic made him pay straight away with a break of his own and went on to take the second set, and the third was completely one-sided as he wrapped up victory after just an hour and 28 minutes.
The Wimbledon champion said: “It’s very windy but I managed to adjust to the conditions. I managed to play better in the important moments, to stay solid and use my serve with accuracy rather than speed. I’m very happy with my performance overall.”
The top seed next plays American Sam Querrey, who upset 28th seed Guillermo Garcia-Lopez 6-3 6-4 6-4.
Ninth seed Jo-Wilfried Tsonga eased to a 6-3 6-4 6-4 win over Aleksandr Nedovyesov, celebrating his win with some shadow boxing rather than his customary dance.
Serena Williams won 10 games in a row to defeat countrywoman Vania King and reach the third round of the US Open. The world number one, who is bidding to win a third straight title at Flushing Meadows, needed just 56 minutes to triumph 6-1 6-0.
Williams dropped only five points on serve in her first-round win over another American, Taylor Townsend, but struggled a little for rhythm on it in breezy conditions on Thursday.
However, she still did enough to not be broken and found King’s serve much to her liking. The 25-year-old managed to hold in the third game but that was as good as it got as Williams turned on the power when she needed it. After disappointing performances in all the grand slams so far this season, the world number one has been focusing on not over-thinking matters here.
And she has been noticeably calmer in her two matches so far. King had her chances in the second set but Williams shut the door every time, more than balancing out the errors with winners.
When King netted the final backhand on Williams’ second match point, she was surely glad that the punishment was over.
Williams, who was wearing a shocking pink leopard-print dress, said: “It’s so hard to play in the wind. I’m really happy to get through a solid match with the conditions today.”
The 32-year-old next meets Varvara Lepchenko, her third successive American opponent.