The 31-year-old, who won last month’s Swedish Open on clay, took eight games in succession on the hard court.
She face Kirsten Flipkens of Belgium next after the 13th seed saw off Kiki Bertens 7-5 3-6 6-2.
Wimbledon champion Marion Bartoli returned from injury to beat American qualifier Lauren Davis 6-0 6-3.
Continue reading the main story “I made a few errors, but it’s just my match on hard in a really long time” Serena Williams Williams, beaten by Sabine Lisicki in the fourth round at Wimbledon, overcame world number 57 Schiavone, 33, for the fifth time in seven meetings.
“I felt solid,” Williams said. “Obviously I made a few errors, but it’s my first match on hard in a really long time. I also played a really good player, so it was a good match.”
Bartoli was scheduled to compete in her first tournament since herWimbledon triumph at the Southern California Open last week, but pulled out with a hamstring injury.
“My hamstring is getting better and better,” said the 28-year-old Frenchwoman, who beat Lisicki in the Wimbledon final last month to claim her first Grand Slam title.
“I just need to take care of it every day. I was able to work with my physio back home and do some rehabilitation and strength work on it so it gets stronger.”
Romania’s Sorana Cirstea, the world number 27, pulled off an upset by beating 10th-ranked Caroline Wozniacki 5-7 7-6 (7-0) 6-4 in a match lasting four minutes short of three hours.
Australian Samantha Stosur, runner-up in the Rogers Cup two years ago and the winner of last week’s event in Carlsbad, saw off Spain’s Carla Suarez Navarro 1-6 6-2 6-3.
Former world number one Ana Ivanovic, winner of this tournament in 2006, beat Anastasia Pavlyuchenkova 6-1 6-4.