The Scot beat 24-year-old Frenchman Corentin Moutet in straight sets 6-2, 7-5, 6-3 after three hours in New York.
Murray's latest triumph marks his 200th Grand Slam victory - the eighth man in tennis history to do so.
Speaking after his win, the 36-year-old said: "It was amazing, a brilliant atmosphere. He (Moutet) is one of the most skilful players on the tour.
"He has so many ways to disrupt you, always causes a little bit of chaos. I hope it was entertaining for everyone."
Murray continued: "I'm glad to get through in straight sets because the second set was very tight. It was a long one, but the way that we play - it was probably always going to be that."
The Scot was in good spirits after the win, joking it was "a lot shorter than most" of his matches this year. "I'm happy to get it done in under three hours," he added.
"I'm at my highest ranking since I had the metal hip put in. I'm happy with that, it has not been an easy journey.
"I'm happy to keep going and progressing and am hoping to push my ranking up."
Murray will meet Bulgaria's Grigor Dimitrov in the second round tomorrow, August 30th, at the US Open.
