The Russian sixth seed was on the brink when Petkovic served at 5-4, 40-0 in the second set of a rain-interrupted scrap on Court One but survived to win 4-6 7-5 6-4.
Petkovic's nerves got the better of her as she wasted all her match points with unforced errors and Kuznetsova, who had been woefully off from, took full advantage.
Kuznetsova also wobbled serving at 5-3 in the decider as Petkovic broke back but sealed victory on her fourth match point in the next game when her opponent drilled a backhand long.
French Open
Men's final could be delayed
08/06/2012 AT 19:46
The Russian will next face compatriot Maria Kirilenko, after the 30th seed beat Yvonne Meusburger 6-3 6-3.
Dane Caroline Wozniacki eased into the third round with a 6-3 6-1 victory over Italy's Tathiana Garbin.
Third seed Wozniacki was rarely troubled on Court Suzanne Lenglen by the world number 56 and relied on her forehand to break five times in a one-sided contest.
She wrapped up the win after 68 minutes when Garbin fired a forehand long.
Wozniacki will next face 31st seed Alexandra Dulgheru for a place in the fourth round, after the Romanian beat Timea Bacsinszky 6-4 6-2.
Venus Williams took another step towards her first French Open title with a routine 6-2 6-4 victory over Spain's Arantxa Parra Santonja.
Wearing an eye-catching black lace corset-style outfit, the second seed bossed most of the rallies as a stiff breeze lashed an overcast Court Philippe Chatrier, coming through in an hour and 35 minutes.
Santonja, who has an unusual double-handed grip on both wings, extended the American with some deft groundstrokes before Williams broke decisively in game seven of the second set, sealing the win when Santonja ballooned a return long.
She next faces Slovakia's 26th seed Dominika Cibulkova, a semi-finalist last year in Paris, who overcame a torrid start to beat American Vavara Lepchenko 4-6 6-2 6-0.
Russian 19th seed Nadia Petrova wasted little time in booking her place in the third round as she dismissed Hungarian Agnes Szavay 6-1 6-2.
Petrova, who has already reached three quarter-finals since the start of the clay-court season, and will next face Madrid champion Aravane Rezai, after the Frenchwoman overcame a minor lapse in concentration during a rain break to beat German Angelique Kerber 6-2 2-6 6-3.
The 15th-seeded Rezai took control of the match but suffered a dip in concentration as play resumed following a rain break, allowing Kerber back into the contest.
Rezai, who beat Justine Henin, Jelena Jankovic and Venus Williams earlier this month to win in Madrid, eventually prevailed on her first match point with a backhand winner after one hour and 43 minutes.
French Open
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French Open
Errani warms up with doubles win
08/06/2012 AT 18:48