But Kvitova, showing the battling qualities that have brought her two Wimbledon titles, fought back to force a decider.
Kvitova, seeded 14th, broke Kerber early in the third set to lead 4-2 and despite struggling with cramp, she held her nerve to convert her seventh match point after three hours and 20 minutes on court.
"At the end I think there is no loser. I did everything today. I was fighting until the end," Kerber told reporters.
Kvitova will face Britain's Johanna Konta in the quarter-finals.
(Reporting by Nivedita Shankar in Bengaluru, editing by Ed Osmond)
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