Kvitova, a former Wimbledon champion, set up a second-round match with Mandy Minella thanks to a 6-4, 6-4 decision over Doi. Kvitova won her only previous encounter with Minella two years ago in Tokyo.
Second-seeded Roberta Vinci also made it to the second round when Andrea Hlavackova retired with an injury during the second set. Vinci had a 6-2, 2-0 lead when Hlavackova retired.
Qualifier Alexandra Cadantu pulled off the day's biggest surprise by disposing of No. 7 seed Sabine Lisicki 7-5, 6-2.
In other second-round action, Petra Martic defeated qualifier Anna Schmiedlova 6-4, 6-2 and Annika Beck fought off Lourdes Dominguez Lino 5-7, 6-3, 6-2.