Isner relied on his power serve, delivering 38 aces in the match to surpass Roger Federer with the second-most career aces, ATP statistics showed.
Isner appeared to feed off the crowd's energy in the fifth set and thanked them for helping him across the line.
"This right here is what the U.S. Open is all about," said Isner. "I couldn't have won this match without the support of you guys," he added, gesturing to the crowd.
Isner later told reporters that the match had been a struggle "from the get-go" but that overall he was pleased with his performance throughout the year.
"I'm certainly very confident. I've had a very good year," Isner said. "I mean, probably the best year of my career. Doing that at 33 is pretty cool."
The three hour and 38-minute match was comparatively light work for marathon man Isner, who in July lost a six hour and 36-minute Wimbledon semi-final to South Africa's Kevin Anderson and in 2010 won an 11 hour and five-minute match against Nicolas Mahut at the All England Club.
Isner next faces Serbian Dusan Lajovic, who beat Briton Cameron Norrie, for a place in the fourth round.
(Editing by Peter Rutherford)
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