Williams was joined in the third round by three other high seeded players who were making their first appearances on the North American hardcourts after the season shifted from Europe.
Wimbledon champion Marion Bartoli beat American Lauren Davis 6-0 6-3, fourth seed Li Na of China joined her following a 6-1 6-4 victory over Anastasia Pavlyuchenkova of Russia while fifth seeded Italian Sara Errani accounted for Klara Zakopalova of the Czech Republic 6-2 7-6(2).
Williams played an aggressive and consistent match to beat Schiavone, whose attempts to serve and volley and mix up her attack had little effect on the 16-times grand slam champion.
“Usually I have a lot of nerves going out there, but in the beginning, I was so relaxed,” Williams, who won a claycourt tournament in Sweden after Wimbledon, told reporters.
“I always feel that way when I’m playing a grand slam champion. I just feel a little bit more relaxed and ready to play.”
Williams will face Kirsten Flipkens of Belgium in the third round after the 13th seed beat Kiki Bertens of the Netherlands 7-5 3-6 6-2.
Bartoli played as well as she did in winning Wimbledon with power hitting and never allowing Davis to grind her down.
“I never played against Lauren before,” Bartoli said.
“I think overall I did pretty well considering the amount of pressure I was under, being the Wimbledon champion and have to step on the court in a tournament where I lost first round the last two times I played.”
The Frenchwoman will face the unseeded Magdalena Rybarikova of Slovakia.
Li, who spent five days after Wimbledon in Munich undergoing medical checks to ensure she was not carrying any significant injuries, did not always employ the high-risk attack her coach Carlos Rodriguez is encouraging her to try out, still managed to out-hit Pavlyuchenkova.
“I was fighting a lot on the court,” said Li, who will face 16th seed Ana Ivanovic of Serbia, a 6-4 6-4 winner over Flavia Pennetta.
“I tried to use more serve/volley but the serve didn’t go in. I was feeling pretty good, because today I tried so many things like not only stay on baseline.”
Sixth seed Petra Kvitova of the Czech Republic ended the hopes of Canadian teenager Eugenie Bouchard 6-3 6-2, while ninth seed Caroline Wozniacki was upset 5-7 7-6(0) 6-4 in nearly three hours by Romanian Sorana Cirstea.
France’s Alize Cornet also ended 11th seeded Russian Maria Kirilenko’s tournament with a 7-5 7-5 victory.
(Editing by Greg Stutchbury)