Second-seeded Kvitova of the Czech Republic won six of the first seven games to take the opening set, before countrywoman Pliskova came back for a 1-6, 6-1, 6-3 victory to advance to the round of 16 in the WTA's first clay-court event of the season.
Kvitova had won 24 straight matches against Czech players before Pliskova's victory.
Pliskova, ranked 77th, is the identical twin of top-10 player Karolina Pliskova, a former world No. 1.
Kristyna got some sisterly advice from Karolina on facing two-time Grand Slam winner Kvitova.
"It really helped because she knows her better than me," said Kristyna Pliskova.
The change, Pliskova said, came when she began to get her serve in over the final two sets.
"First set was horrible, and that's the biggest difference," she said.
Stollar said she was able to dictate points most of the match against Konta.
"I think I pushed my game to her and I stayed really aggressive," said Stollar, who entered the week ranked 219th in singles.
No. 5 seed Julia Goerges of Germany topped American Kristie Ahn 2-6, 6-4, 7-6 (1); No. 8 Anastasija Sevastova of Latvia defeated Caroline Dolehide of the United States in three sets, 7-5, 6-7 (5), 6-1; No. 9 seed Australian Ashleigh Barty ousted Tatjana Maria 4-6, 6-3, 6-2; and No. 10 seed Naomi Osaka of Japan defeated Laura Siegemund of Germany 6-3, 7-6 (8).