The Czech, who was beaten by Andy Murray in the semi-finals of the tournament last year, cruised past the Frenchman with a 6-0 6-3 6-2 win at Flushing Meadows.
"It was a bit hot, a bit humid, but otherwise the tennis was good," Berdych told reporters.
"I managed to stay focused from the first point until the last. There were no ups and downs, just took all my chances that I had, and won in straight sets."
Berdych will now face Stanislas Wawrinka in the fourth round.