Peer, who has a runner-up finish on the tour this year, is making her third appearance in the Stanford, Calif., hardcourt tourney.
Sixth-seeded Frenchwoman Tatiana Golovin ousted Ukrainian Viktoriya Kutuzova 6-2, 6-2; and eighth-seeded Austrian Sybille Bammer topped Japan's Ai Sugiyama 6-4, 6-2. Russian Maria Kirilenko rallied to best Belarusian Victoria Azarenka 3-6, 7-5, 6-4.
Belarusian Olga Govortsova, India's Sania Mirza and Russian qualifier Yaroslava Shvedova also were first-round winners.
The top seeds this week are Russian Anna Chakvetadze and Wimbledon runner-up Marion Bartoli. Bartoli plays a second-round match Wednesday against American wildcard Lilia Osterloh, and third-seeded Slovakian Daniela Hantuchova plays China's Shuai Peng.