World number three Pliskova of the Czech Republic defeated America's 37th-ranked Alison Riske 6-4, 6-7 (4/7), 6-2 as she boosted her hopes of taking the top spot from French Open champion Ashleigh Barty who was knocked out of Toronto on Tuesday.
Japan's reigning US and Australian Open champion Osaka faces Tatjana Maria of Germany in her opening match on Wednesday.
Pliskova, 27, must reach the semi-finals to have a chance at returning to the world number one ranking but if Osaka makes the last-eight, then Pliskova would need to reach the final to stay in contention.
If Osaka loses on Wednesday and Pliskova falls before the semi-finals, then Barty will retain the top ranking.
Pliskova will next play Estonia's 19th-ranked Anett Kontaveit who made the third round when Spain's Carla Suarez Navarro retired with an injury at 7-5, 3-1 down.
In the day's other early second round tie, 19-year-old Dayana Yastremska of the Ukraine defeated two-time major winner and former top-ranked Victoria Azarenka 7-5, 7-5.
Results on Wednesday in the WTA tournament in Toronto (x-denotes seeding):
Dayana Yastremska (UKR) bt Victoria Azarenka (BLR) 7-5, 7-5
Belinda Bencic (SUI x11) bt Julia Goerges (GER) 5-7, 6-3, 6-4
Elina Svitolina (UKR x6) bt Katerina Siniakova (CZE) 6-3, 3-6, 6-3
Karolína Pliskova (CZE x3) bt Alison Riske (USA) 6-4, 6-7 (4/7), 6-2
Anett Kontaveit (EST x16) bt Carla Suarez Navarro (ESP) 7-5, 3-1 -- retired
Simona Halep (ROM x4) bt Jennifer Brady (USA) 4-6, 7-5, 7-6 (7/5)