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. The 37-year-old Williams won the event in 2001, 2011 and 2013 —all in Toronto — and has a match record of 32-4.
"I definitely feel like it takes a while to get back into the rhythm, because we've had a long season of just clay and then grass, and now we're on hard courts," Williams said. "So it definitely feels different, especially for me now. Usually I don't feel that huge of a difference, but for whatever reason I do this year."
The eighth-seeded Williams will face the winner of the late match between No. 2 Naomi Osaka of Japan and Polish qualifier Iga Swiatek.
"I'm feeling good," Williams said. "Just hopefully just being able to stay in the rhythm and playing this week and next week would be good."
Alexandrova staved off 12 break points, but she was broken five times and had 11 double-faults.
"She hit really, really hard and she was hitting a lot of winners," Williams said. "So I was just happy that I was able to just fight through that."
Third-ranked Karolina Pliskova of the Czech Republic advanced to the afternoon, beating Anett Kontaveit of Estonia 6-3, 7-5. In position to reclaim the top spot in the world ranking this week, Pliskova set up a match against Bianca Andreescu of Canada.
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."
Andreescu beat fifth-seeded Kiki Bertens of the Netherlands 6-1, 6-7 (7), 6-4.
The 19-year-old Andreescu, from nearby Mississauga, improved to 5-0 against top-10 opponents this year. A right shoulder injury has limited her to four events since May.
"Being off for that long and coming into the Rogers Cup and getting into the quarterfinals means so much to me," Andreescu said. "And this time off actually helped me. I figured a lot of things out — and it's showing on court."
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 Czech qualifier Marie Bouzkova, a 6-2, 6-2 winner at night over 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.