The two-time Wimbledon champion was two points away from defeat when she trailed the world number 57 at 4-5 in the decider.
But she claimed the next three games to wrap up the win and goes on to face Taiwan's Su-Wei Hsieh for a place in the last 32.
Kvitova committed 10 double faults in a typically rollercoaster display in which she led by a set and had two breaks in the second against an opponent who made the Istanbul final on clay this season.