The 2010 champion and sixth seed needed just an hour to sail through 6-3 6-0 and reach the third round.
She is joined in the last 16 by fifth seed Elina Svitolina, who prevailed 7-6 (7/4) 6-4 against Daria Kasatkina in Tuesday's other second-round match.
Ruthless Collins powers past Cornet into the semi-finals
In the first round, home hope Eugenie Bouchard suffered an early exit. The wild card, ranked 70th in the world, was unable to beat qualifier Donna Vekic, who progressed 6-3 6-4.
Agnieszka Radwanska, winner in 2014 and competing for the first time since her wedding in July, breezed past Coco Vandeweghe 6-3 6-2.
The world number 10's victory sets up a clash with Timea Babos, who saw off 17-year-old Bianca Andreescu 6-4 6-1.
Elsewhere, Anastasia Pavlyuchenkova dropped just one game in a demolition of Alize Cornet, while 16th seed Elena Vesnina beat Alison Riske 6-3 6-3.
Oceane Dodin retired when trailing Ashleigh Barty 5-0 in the opening set while Caroline Garcia battled bast Sorana Cirstea in three sets.
Ekaterina Makarova, Catherine Bellis, Magdalena Rybarikova and Barbora Strycova are also through to the second round.
Order of play, Day 10: Medvedev in top-10 battle, Cornet and Kanepi chase first semis
The must-watch interview and moody Medvedev – AO Diary