Seeded fifth, Kvitova was the third-highest remaining seed in the competition after defeats for Serena Williams and Li Na, but she failed to reach the fourth round for a third time in her six career outings at Roland Garros.
In a match that lasted three hours and 16 minutes, the world number six made 11 double faults as she struggled, especially in the second set, to cope with a thigh injury.
With her right leg heavily strapped, she surrendered her one-set lead meekly before losing out in a 92-minute third set.
Kuznetsova limited her unforced errors to 20, compared to her opponent’s 65, as she beat the 2012 semi-finalist for the first time at the fourth attempt.
Kvitova seized the initial advantage when she broke in the third game, despite wasting a break point, but Kuznestova hit back in the sixth as the opening set edged closer to a tie-break.
The Czech then showed her quality to move three points ahead before clinching the opening set in just over an hour despite making 21 unforced errors.
From there, Kvitova began to struggle with her injury and was forced to take a medical break in a second set where she simply could not keep up with the Russian.
Kvitova won less than half of points on her first service but broke in the first game of the deciding set and went 3-1 ahead.
However, in what was a topsy-turvy finale to the match that saw six more breaks of serve, Kuznetsova booked her progression.
Kuznestova wasted two match points in the 12th but kept her cool to see out the win and book a last-16 meeting with Lucie Safarova.
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