Novak Djokovic revelled in his straight-sets win over Richard Gasquet, the 13-time grand slam champion describing Saturday's victory as his best display at this year's US Open.

Former world number one and Serbian sixth seed Djokovic was relentless and superior in a 6-2 6-3 6-3 round-three win against Frenchman Gasquet on Arthur Ashe Stadium.

Djokovic – a two-time winner at Flushing Meadows – outclassed Gasquet with his impenetrable defence and forehand winners as he made it 11 successive victories over the Frenchman.

After struggling in the heat at the start of the week and having been frustrated by his performance against Tennys Sandgren in the second round, Wimbledon champion Djokovic told reporters post-match: "It was the best match of the week so far, without a doubt.

"One of the best performances I had in the hard-court season after Wimbledon. Came at the right time because Gasquet is a tricky player, someone that has plenty of experience, someone that I know very well. Obviously he showcased today why he has one of the best backhands, one-handed backhands, in the game.

"I don't think he was playing bad. He was there. It seemed like he just needed a few points to break through. I was lucky to really save some crucial break points in the third set. If he got back that break, who knows. He was playing well.

"I thought I was playing on a very high level from the first point. Very, very pleased with the performance."

Standing in the way of Djokovic and the US Open quarter-finals is unseeded Portuguese veteran Joao Sousa, who upstaged Lucas Pouille on Saturday.

"He made a good win a few days ago, today against top-15 player," Djokovic said. "He deserves a credit for reaching first time last 16 in a slam.

"He doesn't have anything to lose. He's a fighter. He grinds. He doesn't give you too many free points. He makes you run. He loves to run. Loves to run around his backhand, hit some forehands. Plays pretty flat.

"I've played him. I think I played him here many years ago. Haven't played him for a while. Anyway, look, I know that I'm clear favourite in the match. At the same time I will try to maintain the level of focus and performance and level of tennis that I've had today. If it's like that, then I have a good chance to win.