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.
After it turned out that Deputy Prime Minister Andrei Belousov included the Fonbet betting company in the list of backbone enterprises that can count on state support, everyone started talking about these bookmakers.