New York: Novak Djokovic enjoyed his first routine victory at this year's US Open at the third attempt on Saturday as the two-time champion eased into the fourth round with a 6-2 6-3 6-3 win over flamboyant Frenchman Richard Gasquet.

The sixth-seeded Serb needed four sets to despatch his first two opponents, struggling especially in the opening round against Hungarian Marton Fucsovics in searing daytime temperatures at the start of the week.

However, the Wimbledon champion started brightly under the floodlights at Arthur Ashe Stadium against the 26th seed and never looked back, sealing a comfortable triumph in two hours and 11 minutes.

"It was my best match of the week so far, without a doubt," Djokovic told reporters. "One of the best performances I had in the hard court season after Wimbledon.

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

Djokovic won 75 per cent of his first serves, struck 32 winners and saved each of the five break points he faced as the 32-year-old Gasquet's game collapsed under the weight of his 47 unforced errors.

The win marked the 13th time Djokovic had beaten Gasquet in 14 meetings, with the Serb winning his last 11 matches against the Frenchman.

Victory keeps the 13-times Grand Slam champion on track for a potential quarter-final showdown against second seed Roger Federer, who saw off Nick Kyrgios in straight sets earlier in the day.

Next up for the Serb, however, is a last-16 clash with unseeded Portuguese Joao Sousa.

"He's a fighter, he's a grinder," Djokovic said. "He will not hand you the victory, you've got to earn it... I'm really glad I didn't spend too much time on the court tonight. I'm going to get some rest and move on to the next one."

"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." 

Meanwhile, seventh seed Marin Cilic was forced to recover from two sets down to battle past Australian teenager Alex de Minaur 4-6 3-6 6-3 6-4 7-5 in a marathon contest that went deep into the night at the US Open on Saturday.

Cilic, the 2014 champion, may have been justified in expecting an easier pathway past the third round, but the 19-year-old De Minaur has already earned a reputation for having an abundance of fighting spirit in his relatively short career.

Where his compatriot Kyrgios slumped to a tame loss at the hands of Federer earlier in the day, De Minaur started on the front foot, running down everything Cilic sent over the net to carve out a 2-0 lead.

Cilic rallied behind his big serve but De Minaur made the Croatian work hard for every point all the way to the bitter end at 2.22am local time (0622 GMT), only a few minutes short of the latest ever finish at the US Open.

"Incredibly happy, it was just an insane atmosphere," Cilic said on the Louis Armstrong Stadium court after setting up a last 16 meeting with David Goffin.

"Incredible fighting spirit. He played some amazing tennis. I was just a little bit luckier today.

"It doesn't get any better. What time is it? Two-thirty in the morning and everybody staying around? To come from two sets down, it's one of the best matches in my career."

Trailing 5-2 in the final set and serving to stay alive, De Minaur staved off five match points to force Cilic to win the match on his own serve, and then saved another before breaking the Croatian and bringing the score to 5-4.

He held on to level at 5-5 before Cilic held to love and broke again to seal the match on his eighth match point in three hours and 59 minutes.

Cilic hit 14 aces to De Minaur's four but the Croatian, who won 73 per cent of his first serves, was undermined by inconsistency, making 70 unforced errors.

Both players were neck-and-neck from the baseline, but De Minaur's gritty performance was well reflected by the fact that he saved 20 of the 28 break points he faced.

In the end the crowd were firmly on the fresh-faced youngster's side, willing him on to victory and giving him a standing ovation as he walked off the court in defeat at the end of the epic contest.