In position to reclaim the top spot in the world ranking this week, Pliskova set up a match against Bianca Andreescu of Canada. Andreescu beat fifth-seeded Kiki Bertens of the Netherlands 6-1, 6-7 (7), 6-4.
Pliskova finished off Kontaveit in two sets after taking three against American Alison Riske on Wednesday.
“For sure better than it was maybe yesterday,” Pliskova said. “So I guess it’s going to get better every day with what I play. And I always was, I am, improving with matches.”
The 19-year-old Andreescu improved to 5-0 against top-10 opponents this year.
Playing her first event since losing the Wimbledon final, Williams opened with a 6-3, 6-3 victory over Elise Mertens of Belgium on Wednesday night. The 37-year-old Williams has won the event three times, all in Toronto.
Fourth-seeded Simona Halep of Romania, making her first start since beating Williams for the Wimbledon title, beat Svetlana Kuznetsova of Russia 6-2, 6-1. Halep will face the winner of the night match between Czech qualifier Marie Bouzkova and Latvia’s Jalena Ostapenko.
American Sofia Kenin beat Ukrainian teenager Dayana Yastremska 6-2, 6-2. Kenin beat top-ranked Ashleigh Barty in the previous round. In the quarterfinals, Kenin will face sixth-seeded Elina Svitolina of Ukraine, a 6-2, 6-4 winner over 11th-seeded Belinda Bencic of Switzerland.