Fourth-seeded Victoria Azarenka of Belarus, the highest-remaining seed in the women's draw, also reached the quarterfinals on Monday. Azarenka matched her best result at a Grand Slam tournament by beating Ekaterina Makarova of Russia 6-2, 6-3.
The seventh-seeded Sharapova has won the other three major tournaments once each but is still looking for her first title at Roland Garros.
Against Radwanska, the 2006 French Open junior champion, Sharapova fell behind 4-1 in the first set and 5-3 in the second before turning things around. Sharapova saved five set points in the second.
The Russian was the more aggressive player and finished with far more winners, 47-13, and unforced errors, 44-12.
The 15th-ranked Petkovic stretched her winning streak to nine matches, including a clay-court title at Strasbourg the week before play began at Roland Garros.
Petkovic never had been past the second round at the French Open.
The sixth-seeded Li was trailing 3-0 in the third set when her husband Jiang Shan, who is also her former coach, left Court Philippe Chatrier. Li then won the final six games to beat Kvitova.
"I don't know what happened. Maybe it's just my husband left and I was able to win six games in a row," joked Li, who became the first Chinese player to reach the quarterfinals at Roland Garros.
After falling in the Australian Open final to Kim Clijsters, Li lost four consecutive matches and decided it was time to stop the slide.
She started working with new coach Michael Mortensen in April before the Madrid Open, and their collaboration immediately paid off as she reached the semifinals in the Spanish capital.
Li said she needed a break from her husband both on and off the court after three years of working together. She said she tried not to hurt her husband -- now her hitting partner -- when she told him their collaboration was over and said she didn't use the word "fired."
"I would never say that," she said. "I mean, it's tough. ... So I tried to never say, 'I fire you."
Kvitova broke the sixth-seeded Li twice in the opening set Monday, but the ninth-seeded Czech dropped serve twice in the second set as Li won five games in a row to even the score.
Li lost her serve in the second game of the final set when she double-faulted, but Kvitova failed to extend her lead as the Czech player lost the final six games of the match.
"I was really in trouble," Li said about her difficult start to the third set. "I didn't believe I could come back, because she has a huge, big serve. But I was OK. She had just broken once."
Information from The Associated Press was used in this report.