Williams, looking to add the title at Flushing Meadows to those she won at Wimbledon and the Olympics this year, has lost 16 games through her first five matches.
Against Ivanovic, fourth-seeded Williams faced only two break points and saved both. Leading 4-3 in the second set, Williams got taken to three deuces but closed out the game with a pair of service winners clocked at 119 and 105 mph.
Ivanovic was making her first appearance in a Grand Slam quarterfinal since winning the French Open in 2008.
Williams' next match is against Sara Errani, the French Open runner-up this year, who beat Roberta Vinci 6-2, 6-4.