
Mauresmo missed much of 2007 after February abdominal surgery which left her struggling for the rest of the season. The year before, she won two Grand Slams, in Melbourne and Wimbledon.
The win took the Swiss 76 minutes. Mauresmo held a 12-5 lead in their series, winning the last five meetings dating to 2004.
Schnyder, 16th in the world, next faces China's Li Na, who upset top seed Nicole Vaidisova 6-3 6-3.
Vaidasova was troubled with an ankle injury in the opening set. "She played a great game before that happened," said the seed. "It's not my excuse for losing."
Holder Dinara Safina was eliminated,a victim of fifth seed Shahar Peer 4-6, 6-1, 7-6 (10-8).