Two-time grand slam champion Kvitova was comfortably beaten in straight sets by Irina-Camelia Begu, with the Romanian winning 6-4 6-0 in just one hour and nine minutes.
The effectiveness of the first serve was the main difference-maker, with Begu winning 73.1 per cent of her first-serve points, while Kvitova – who has 28 singles titles to her name in contrast to her opponents' four – could only manage 50 per cent.
Begu was set to face the winner of Tereza Martincova's tie with Elena Rybakina, but the latter withdrew because of illness.
Seventh seed Ostapenko made light work of Andrea Petkovic as she beat the German 6-1 6-2 in just 58 minutes, helped largely by winning 85.3 per cent of her first serves, as well as saving all five of the break points she offered up.
Ostapenko has now won two of her four meetings with Petkovic and will next face Aliaksandra Sasnovich, who eased to a 6-2 6-3 victory over Jaqueline Cristian.