Czech Pliskova won 86% of her points on her first serve and needed only two break points to beat Romania's Mihaela Buzarnescu 6-3 6-4 in a match that lasted just 69 minutes.
Fifth seed Sabalenka of Belarus lost 6-3 2-6 7-6(1) to Hsieh Su-wei after the Taiwanese came from a break down at 4-2 in the final set to eventually clinch victory in the tiebreak.
"It was not easy because it's my first match on the grass court," Hsieh said. "I knew it was going to be really tough, so I just got ready for anything to happen on the court.
"It's not easy because you know she can make any winner from anywhere -- serve, return, baseline. She was slicing pretty good, I was surprised."
Ukrainian fourth seed Svitolina lost 6-3 3-6 6-4 to Margarita Gasparyan in the Russian's second win over a top 10 player in her career. Svitolina did herself no favours with five double faults and 15 unforced errors in the first set alone.
Local favourite and French Open semi-finalist Johanna Konta, seeded seventh, breezed into the second round with a 6-4 6-2 victory over Anett Kontaveit of Estonia.
Top seeds Naomi Osaka and Ashleigh Barty are in action on Tuesday against Maria Sakkari and Donna Vekic respectively.
(Reporting by Rohith Nair in Bengaluru; Editing by Ken Ferris)
