Peer advanced with a 6-2, 5-7, 6-4 win over Elena Likhovtseva Tuesday in the first round of the grass-court tournament and is paired against Aiko Nakamura in the second round.
Seeded players Marion Bartoli and Sybille Bammer also won Tuesday. Bartoli had little trouble in a 6-2, 6-3 win over Tathiana Garbin and Bammer posted an identical 6-2, 6-3 decision over Maria Kirilenko.
World No. 1 and event defending champion Justine Henin is the top seed for the tournament while Amelie Mauresmo is seeded second. They open their play on Wednesday.
Millions of Getty images now available for free via embed tool
NBC reportedly holds celebs hostage to Jimmy Fallon's show