The fourth-ranked Petrova, who is 11-0 on clay this year on the WTA Tour, beat Vera Zvonareva of Russia 6-1, 7-6 (3), while Hingis ousted Julia Schruff of Germany 6-4, 6-3.
Petrova's only loss on clay this year came against Justine Henin-Hardenne two weeks ago in the Fed Cup. On tour, three titles in her last four events have made her one of the French Open favorites.
The 23-year-old Russian stroked a backhand volley into the open court at match point after Zvonareva scrambled back from 1-3 down to force the second-set tiebreaker.
"I'm a completely different person this year - win or lose it doesn't bother me," Petrova said.
When Petrova lost last year's final to Henin-Hardenne in three close sets, she still hadn't won a singles title. Since then, the Russian said she had learned to have more fun on court.
Defending champion Henin-Hardenne beat Italy's Mara Santangelo 6-4, 6-1. Top-ranked Amelie Mauresmo needed just 59 minutes to roll past Vera Dushevina of Russia, 6-1, 6-2.
Mauresmo played her first match since taking a break in late March.
"I was not expecting to play my best tennis, but I expected to play solid tennis, and I did that today," Mauresmo said.
Hingis set up a third-round meeting with eighth-ranked Elena Dementieva, who was leading Julia Vakulenko 6-3, 2-0 when the Ukrainian pulled out injured.
The former top-ranked player from Switzerland lost to Dementieva 6-2, 6-0 in Tokyo - her only final since coming back in January after injuries forced a three-year hiatus.
Hingis said she was hoping the result would be different on clay.
"I have nothing to lose - I only won two games, but you have to believe in yourself," Hingis said.
Switzerland's Patty Schnyder, seeded fourth, beat Estonia's Maret Ani, 6-1, 6-4, and No. 8 Daniela Hantuchova of Slovakia outlasted Katarina Srebotnik of Slovenia, 6-4, 0-6, 6-1.
Three other Russians also advanced. Sixth-seeded Svetlana Kuznetsova beat Martina Muller of Germany 6-3, 3-6, 6-0, No. 15 Maria Kirilenko downed Klara Koukalova of the Czech Republic 6-4, 6-3 and Anna Chakvetadze upset 16th-seeded Anabel Medina Garrigues of Spain 6-3, 6-4.
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