The former world number one, playing her first match since Wimbledon, held off a second-set fightback from Ivanovic, the world number 15, to clinch victory in 71 minutes.
"I only started practising two weeks ago so I'm very happy with the way I played," Williams said.
Having not played since Wimbledon due to a wrist injury, Williams made a slow start, dropping serve in the opening game.
But the American, whose ranking has fallen to 54, broke back for 2-2 and broke again in the eighth game before serving out the first set.
Ivanovic, who won the U.S. Open Series, recovered an early break at the start of the second set but Williams broke twice more to lead 4-1.
The Serbian got one break back and had two break points to level at 5-5 but Williams held on to set up a second-round meeting with Polish qualifier Agnieszka Radwanksa, who beat Italian Mara Santangelo 5-7 7-6 6-3.
Top seed Elena Dementieva of Russia made a solid start to her title campaign as she beat Australian Samantha Stosur 7-5 6-1 and will next meet the winner of the Williams-Radwanksa match in the quarter-finals.
Third seed Patty Schnyder crushed American Chanda Rubin 6-0 6-3 to reach the last eight, hitting six aces as she raced to victory inside an hour.
The Swiss will now play fourth seed Dinara Safina of Russia, who edged out Slovakian Daniela Hantuchova 7-5 6-3.
Italian qualifier Karin Knapp, who beat last year's runner-up Anna-Lena Groenefeld of Germany in round one, lost 6-4 6-4 to Czech Kveta Peschke.
