Kvitova overcame a few nervy moments at the beginning, as well as a rain-enforced stoppage, to win in straight sets.
The tournament also saw its first shock as 20th seed Bernard Tomic went out to David Goffin and there was disappointment for Londoner Laura Robson, who lost to world number 26 Francesca Schiavone.
In other results Jo-Wilfried Tsonga beat Lleyton Hewitt, Serena Williams thrashed Zahlavova Strycova and 11-time grand slam winner Rafael Nadal overcame a poor start to see off Thomaz Bellucci.