Fourth-seed Nicole Vaidisova progressed with a 7-6, 6-0 win over Italy's Mara Santangelo, while fifth-seeded Serbian Ana Ivanovic fought off four set points to edge out Michaella Krajicek 6-1, 7-6.
Sixth seed Jelena Jankovic was kept on court for over two hours for a 6-1, 6-7, 6-3 victory over Austrian Sybille Bammer.
Petrova faced a potentially challenging task against Peer, who has won three titles in 2006 and defeated opponents such as Elena Dementieva and Anastasia Myskina.
But the second-seeded Russian hardly broke into a sweat as she outplayed Peer with a solid game, seven aces and accurate groundstrokes.
Peer managed to salvage only three points from the first three games, Petrova breaking for 2-0 when the Israeli netted a forehand.
A double-fault gave Petrova a second break to lead 5-1 and she served out to love, hitting her fourth ace on set point.
Peer briefly threatened in the second set, twice taking Petrova to deuce before the Russian held for 1-1.
Petrova's response was to break Peer twice to lead 4-1 and she wrapped up the match by dropping one point in the last three games.
"Before I came on court I thought it was going to be very tough, and the way I approached this match I decided to keep it as short as I could by trying to put pressure on her," Petrova told reporters.
"I didn't do anything wrong but I don't feel I did anything spectacular. I just tried to take the opportunities."
Krajicek has inherited the serving prowess of her brother, former Wimbledon champion Richard, but found it counted for nothing against Ivanovic.
LOST PACE
The Serb dominated the first set with some stunning returns, breaking Krajicek to love in the opening game before racing to a 4-0 lead. A crosscourt backhand earned her a further break for the set.
Ivanovic lost some of her pace on the returns in the second and Krajicek settled into trading groundstrokes.
After four consecutive breaks early in the set, Krajicek held off two match points at 4-5 and broke to lead 6-5. But she was unable to convert the four set points she earned in a lengthy game that stretched to six deuces. Ivanovic swept the tiebreak for the loss of just two points.
Vaidisova failed to capitalise on three break points at 1-1 and four more at 2-2 as she faced Santangelo. But after being taken to a tiebreak, Vaidisova eventually broke for 2-0 in the second set on her ninth break point of the match and then took control.
Jankovic also failed to build on a good start after she gave up just five points in the first five games against Bammer.
She became increasingly frustrated in the second set as she failed to hold on to two service breaks.
She almost suffered a repeat in the final set, breaking for 3-1 but then fighting off eight break points, including three as she served for the match at 5-3.
Greek qualifier Eleni Daniilidou beat American Chanda Rubin 6-1, 6-2 to earn a second-round clash with top seed Maria Sharapova.
Slovak Daniela Hantuchova retired with a rib injury with Russia's Elena Vesnina leading 4-3.
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