TORONTO, Canada -- 23-time Grand Slam champion Serena Williams moved into the Rogers Cup quarterfinals on Thursday night by staving off Russian qualifier Ekaterina Alexandrova, 7-5, 6-4.

Williams keeps her quest for the fourth Rogers Cup title of her career alive after her one-hour and 31-minute victory over Alexandrova. The former World No.1 won the tournament in 2001, 2011, and 2013, and now has a sublime 32-4 win-loss record at the event.

Read more: ‘Pain-free’ Serena looking for ‘momentum’ in Rogers Cup return

"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, in her post-match press conference. "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."

"But, yeah, I'm feeling good," Williams continued. "Just hopefully just being able to stay in the rhythm and playing this week and next week would be good."

Powerful Russian Alexandrova, ranked World No.48, had more winners than Williams, by 24 to 18. However, Williams was more solid in her service games, winning nearly 80 percent of points on her first delivery and firing six aces in the clash. Alexandrova was able to stave off 12 break points, but she was still broken five times and hit 11 double faults overall.

"[Alexandrova] hit really, really hard and she was hitting a lot of winners," Williams noted. "So I was just happy that I was able to just fight through that."

It was Alexandrova who got off to a hot start, as the hard-hitting Russian broke Williams in the opening service game. Alexandrova then reached a commanding 3-0 lead after breaking the American for a second time, with a backhand crosscourt winner on break point.

After attaining one of the breaks back in the subsequent game, Williams’s service started to click, and she blasted two aces en route to a hold for 3-2. Williams then reached parity in the next game after Alexandrova hit back-to-back double faults to drop serve once more.

From there, Williams was unbothered on serve for the rest of the set, and after two breezy service games, the American held three set points on Alexandrova’s serve at 5-4. But bold aggression by the Russian paid off, erasing those chances with two winners down the line and a strong serve, and she held for 5-5 with another down-the-line winner.

Williams, however, would get another chance in Alexandrova’s next service game, as unforced errors by the qualifier gave the American a fourth set point. There, Alexandrova hit her eighth double fault of the set, and Williams had successfully notched the opening frame.

37-year-old Williams was broken in the first game of the second set, meaning she was down a break in all four of the sets she has contested this week. However, the American was able to eventually win all of those sets, and this would turn out to be no exception. She began her fightback in the second set by breaking Alexandrova to pull level at 3-3.

Reminiscent of her grit in the opening set, Alexandrova dodged three match points on her serve at 5-4 with risky, aggressive play, punching the third one away with a winning volley. But Williams garnered a fourth match point in the game with a backhand winner, and the Top 10 star converted that chance with a forehand winner down the line to collect another victory in Toronto.

In the quarterfinals, Williams will face the winner of the nightcap match between No.2 seed Naomi Osaka and Polish qualifier Iga Swiatek. "It will be a good match, whoever wins," said Williams. "Both players are playing well in this tournament in particular, so I'll be ready for her."