The sixth-seeded Kuznetsova won 4-6, 7-5, 6-4 on Wednesday in a match interrupted by a 1½-hour rain delay.
After taking the first set, the 41st-ranked Petkovic led 4-2 in the second and served for the match at 5-4. The German went ahead 40-0 but sent a backhand into the net, a forehand long and a backhand wide to waste three match points. On her fourth, she put another backhand into the net.
Eventually, Kuznetsova hit a backhand passing shot to break serve, part of a five-game run for the Russian.
"I'm not really sure what happened," Kuznetsova said. "I saw that she got tight."
Up 5-2 in the third, Kuznetsova had trouble closing it out. But she converted her fourth match point.
"I move on much more confident from being in that hole," Kuznetsova said. "I stood up there strong."
No. 2-seeded Venus Williams used her big serve to beat Arantxa Parra Santonja 6-2, 6-4. Williams whiffed on a forehand and was often bested in long rallies, but serves at up to 128 mph kept her in control, and she was never broken.
"On the bigger points, especially on my serve, I thought I played those really well," Williams said. "I think that was key."
Williams improved to 14-2 on clay in 2010. She's seeded second behind her younger sister Serena, who scouted while sitting next to their father. The sisters could meet in the final.
In other women's play, No. 3 Caroline Wozniacki defeated Tathiana Garbin 6-3, 6-1; two-time semifinalist Nadia Petrova, seeded 19th, beat Agnes Szavay 6-1, 6-2; No. 14 Flavia Pennetta defeated Roberta Vinci 6-1, 6-1; 15th seed Aravane Rezai held off Angelique Kerber 6-2, 2-6, 6-3; No. 30 Maria Kirilenko beat Yvonne Meusburger 6-3, 6-3; No. 31 Alexandra Dulgheru beat Timea Bacsinszky 6-4, 6-2; and No. 26 Dominika Cibulkova rallied past American Varvara Lepchenko 4-6, 6-2, 6-0. Cibulkova, a semifinalist last year, faces Williams next.
For the day's opening match on center court, Williams again wore her black lace dress with bright red trim despite a brisk change in the weather, with mostly cloudy skies and temperatures in the 60s. At her postmatch news conference, there were seven questions about her outfit.
Williams said the corset-like outfit's overlay and skin-toned undergarments are "about the illusion of bareness."
"Lace has never been done before in tennis, and I've been wanting to do it for a long time," she said. "The illusion of just having bare skin is definitely for me a lot more beautiful."
French Tennis Federation spokesman Christophe Proust said: "It gives the illusion that she's naked [underneath], but she isn't. Maybe some people didn't like it, but from what I know there was no angry reaction from the organizers or French federation officials."
WTA spokesman Andrew Walker said Williams' outfit is "not a violation of our match attire rules."
Williams sent her flounce flying when she served. She went to deuce six times in her first service game before holding and then pulled away to take the set.
In the second set, both players held until the seventh game. Williams drew Parra Santonja into a moonball rally, then sprinted forward to slam a winner. That gave Williams a 4-3 lead, and she served out the victory, her 28th in 32 matches this year.
In 13 previous French Open appearances, Williams reached the semifinals only once -- in 2002, when she lost to Serena in the final. But at 29 she's enjoying a career resurgence, and her record this year is the best on the women's tour.
"I'll continue to try to execute my game and not worry really a ton about what my opponent is doing," Williams said.
Information from The Associated Press was used in this report.