Australian No.1 Alex de Minaur is into the third round of the US Open after seeing off French veteran Richard Gasquet in a tough four-set encounter.

De Minaur looked on course for a regulation victory after cruising to a two-set lead and held three match points in the third, only for Gasquet to to win the last five points of the tie-breaker.

The 2013 semi-finalist then raced into a 3-0 lead in the fourth set following an early break of the 21st-seeded de Minaur’s serve.

But the fleet-footed Sydneysider showed all his renowned fighting qualities to level the set in sweltering conditions in New York and then broke the former world No.7 at 6-5 to win a tense three-hour encounter 6-4 6-3 6-7 (8-6) 7-5.

The 34-year-old Gasquet was visibly wilting in the latter stages of the match as the on-court temperatures nudged 35 degrees and de Minaur said he knew he had the stamina to see him off.

“It was a tough battle out there, Richard played a great game but I back my fitness against anyone and that really helped me out today,” de Minaur said.

De Minaur, who reached the fourth round at Flushing Meadows last year, will now face giant Russian 11th-seed Karen Khachanov for a place in the fourth round.

The 198cm tall Khachanov, who lost in a titanic, five-set Australian Open third-round clash against Nick Kyrgios last January, booked his last-32 spot with a comfortable 6-3 6-4 6-1 win over compatriot Andrey Kuznetsov.

Saturday’s encounter will be the first time the pair have met and de Minaur knows he will face a vastly different test against the hard-hitting world No.16 to what he encountered against the tigerish Gasquet.

“He is a big guy who likes to hit the ball very big,” he said.

“The most important thing for me is to not get dictated to and I have to stand my ground and make my presence felt.

“If I can do that then I can go well, but it is going to be a very tough match.”

Fellow Australian later John Millman lost a brutal second-round baseline slugfest to bow out of the US Open in New York.

Australia’s 2018 quarter-finalist was unable to convert a two-sets-to-one lead on Friday, going down 7-6 (8-6) 3-6 1-6 6-3 6-3 to talented young American Frances Tiafoe.

Millman’s exit leaves De Minaur, Jordan Thompson and Chris O’Connell – who plays Russian Daniil Medvedev later on day four – to fly the Australian flag in the singles.

-with AAP