In sweltering conditions in New York, he recovered from a poor start to beat Frenchman Adrian Mannarino in five sets.
He'll face Brazilian 30th seed Thomaz Bellucci next.
Britain's Johanna Konta, meanwhile, secured a history-making win.
She beat ninth seed Garbine Muguruza in a deciding set, of a contest which lasted 3 hours and 23 minutes.
That's the longest women's match at the tournament since tie-breaks were introduced in 1970.
British number two Aljaz Bedene was beaten by American Donald Young.
Meanwhile, Rafael Nadal faces a dangerous opponent in the third round of the US Open tennis later.
Italy's Fabio Fognini has beaten the 14-time grand slam champion twice this year.
