The Swiss 17-time grand slam champion had a third-set hiccup but recovered to win 6-4 6-4 6-4 under lights on Arthur Ashe Stadium.
Groth's big serve was expected to test second seed Federer, yet it barely troubled him.
Federer ended up with more aces (9-8) and broke serve five times in one hour 48 minutes.
He hit 36 winners to set up a meeting with Spaniard Marcel Granollers, a player Federer has beaten in straight sets in their previous two meetings.
Federer broke Groth in the seventh game of the opening set before they traded breaks to start the second.
Groth dropped serve again in the ninth to give up the set, but did look on track to extend the match in the third.
The Australian went 4-2 up, only to lose four straight games as Federer eased through at Flushing Meadows.