Konta, who will be seeded for the first time at Wimbledon this year, overcame her Ukrainian opponent 7-6 (7-4) 6-1.
Kvitova won her only previous meeting with Konta, coming through 7-5 6-3 in the US Open last 16 in September.
Top seed Agnieszka Radwanska and former world number one Caroline Wozniacki also advanced to the third round.
Mirjana Lucic-Baroni of Croatia was forced to retire from her match against Poland's Radwanska because of illness while trailing 6-4 2-1. Dane Wozniacki - now ranked 37th in the world - produced a superb performance to beat Australian Sam Stosur 6-2 6-1.
