Ninth seed Tsonga, 31, breezed through the first two sets but 26th-seeded Sock forced a third-set tiebreak and fought off a match point before taking it 9-7.
That was merely a delay of execution for Sock, though, as his French opponent quickly finished the job for a 6-3 6-3 6-7(7) 6-2 victory.
The Frenchman won on his third match point when Sock sent a forehand wildly beyond the sideline and celebrated with a jumping spin and some fist pumps.
Tsonga, the 2003 U.S. Open junior champion, will next play either top seed Novak Djokovic or unseeded Briton Kyle Edmund, seeking his first U.S. Open semi-final after reaching semi-finals at each of the other three grand slam championships.
"I'm in quarter-final and now anything can happen," said a grinning Tsonga in an on-court interview.
(Editing by Andrew Both)
