Sam Stosur, Francesca Schiavone, Victoria Azarenka and Elena Dementieva also won but Dinara Safina was beaten.
Mauresmo and Nathalie Dechy are paired against Vera Douchevina and Dinara Safina in Sunday's doubles.
Petrova will face Russian compatriot and fifth seed Dinara Safina, who beat Katarina Srebotnik of Slovenia 6-3 6-1.
Current No. 1 Dinara Safina avoided any embarrassment with a 7-5 6-1 victory over unseeded Belgian Kirsten Flipkens.
The unseeded German reached her second final in two weeks with a 6-4 5-7 6-4 upset win against Dinara Safina.
The No. 1 ranked player the past three years has included Ana Ivanovic, Jelana Jankovic, Dinara Safina and Carolyn Wozniacki.
World number one Dinara Safina was sent packing 7-6 4-6 7-5 by teenage qualifier Chang Kai-Chen, ranked 132nd in the world.
The three-set 6-4 3-6 6-3 victory also assures Serena of keeping the world number one spot ahead of Russian Dinara Safina.
Dinara Safina got three more titles since taking over the top spot.
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"I think Dinara should be the number one seed, " said the American.
Second seed Dinara Safina beat fellow Russian Elena Likhovtseva 6-3 6-2.
Home hopes will be carried into the next round by Zheng Jie and Li Na, who play Dinara Safina and Kaia Kanepi of Estonia respectively.
But former world number one Dinara Safina's poor form continued as she was dumped out of the competition by Romanian Alexandra Dulgheru, losing 6-4 6-7 6-1.
In Kazakhstan, Timur Kulibaev and his wife Dinara Kulibaeva, the daughter of President Nursultan Nazarbaev, jointly own 60% of Halyk Bank through their investment vehicle Almex.
The Belgian faces a quarter-final clash with Russia's Dinara Safina.
After Dinara Safina got to No. 1, she won three more titles and has since dropped off the Tour with injuries (she hasn't played in more than a year).
World No. 5 Williams, seeded third in the absence of her top-ranked younger sister Serena and No. 2 Dinara Safina due to injuries, crushed unseeded German Sabine Lisicki 6-2 6-3.
World No. 2 Dinara Safina cruised into the fourth round with a 6-1 6-2 win over unseeded Elena Baltacha of Britain, and will next play fellow Russian Maria Kirilenko.
It was a marked improvement on last year, however, when she had the misfortune to draw world number one Dinara Safina in the first round and failed to win a game.
In the final first-round ties, world No. 2 Caroline Wozniacki crushed qualifier Petra Kvitova 6-4 6-2, while third-ranked Dinara Safina suffered a shock 7-6 7-6 defeat against Czech qualifier Kara Zakopalova.
Baltacha, making her main draw debut at Roland Garros, must have feared a repeat of compatriot Anne Keothavong's 6-0 6-0 'double bagel' defeat by Dinara Safina at last year's French Open.
Meanwhile, top seed Dinara Safina's quest to win her first Wimbledon title may be scuppered by a knee problem she suffered in her first round victory over Lourdes Dominguez Lino of Spain.
The next Motorola Atrix phone has been revealed on the company's website as the Atrix HD, with an MB886 model number matching the "Dinara" we saw pass through the FCC.
ENGADGET: Motorola Atrix HD revealed with 4.5-inch Colorboost HD display, ICS and Droid RAZR looks
Sixth seed Elena Dementieva will not be able to take advantage of world No. 3 Dinara Safina's upset defeat on Tuesday, as she lost 6-1 7-6 (7-5) to former No. 1 Ana Ivanovic.
The match also marked the first time since two years earlier, when Serena Williams beat Dinara Safina on the same court, that a Grand Slam title placed a new player atop the rankings.
Last year's runner-up and second seed Dinara Safina was made to battle for her first win beating Magdalena Rybarikova 6-4 6-4 in 89 minutes, while fellow-Russian and third seed Svetlana Kuznetsova was a straight-sets winner over Anastasia Rodionova 6-1 6-2.
Becker bemoaned the fact that Dinara Safina was installed as world number one for much of last year, despite never winning a grand slam, and said Clijsters remarkable return to claim the U.S. Open came not a minute too late.
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It was a routine win for the tournament favorite Serena -- in stark contrast to the New York hopes of Russian trio Dinara Safina, Maria Sharapova and Elena Dementieva who have all crashed out of the tournament in the last couple of days.
Serena, who will end the year as world No. 1 after Dinara Safina pulled out of the tournament with a back injury on Wednesday, won her third successive match in the Maroon Group with a 6-2 6-4 demolition of Elena Dementieva on Thursday.
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