One of the shortest players in the ATP's top 100, Schwartzman, who is 25 and from Argentina, produced another towering performance at Flushing Meadows.
Seeded 29 in the men's singles, Schwartzman, who stands at 5ft 7", won the first set on a tie-breaker (7-3) and he built on some enthralling tennis to take a 2-0 love lead after winning the second 7-5.
To his credit, Pouille battled back to win the third 6-2, but Schwartzman showed great character to bounce straight back and see out the match, taking the fourth 6-2 in a contest that lasted more than two and a half hours.
Schwartzman will meet 12th seed Pablo Carreno Busta, conqueror of Israeli born Dennis Shapalov, for a place in the semi-finals.
Israel retains interest in the men's doubles, where Dudi Sela and Steve Darcis of Belgium have reached the third round. They face Robin Haase and Matwe Middelkoop