TORONTO, Canada - No.5 seed Elina Svitolina scored her first-ever win against Venus Williams on Thursday night in emphatic fashion, 6-2, 6-1, to move through to the quarterfinals at the Rogers Cup.

"I was just trying to focus on my game and play one point at a time," Svitolina said on-court. "I was just trying to be there in the right moment, move quick, look for the ball and play as deep as I could to make her feel uncomfortable. I needed to stay calm tonight and just really be focused on each point. I'm very happy that I could win in straight sets."

In the second career meeting between the two players, Svitolina was in command from the get-go as she built a 5-0 lead in the opening set and never looked back.

The Ukrainian hit 14 winners to just 10 unforced errors in a clean performance, while Williams struggled to find her range off of relentless defensive pressure from the World No.5 and accumulated 21 unforced errors to just six winners.

"I know Venus for many years, and, you know, when they announce that she turned professional in 1994 and I was just born in this year, I was like, 'Okay, then I need to work really hard in this match,'" Svitolina said. "It was a great privilege to share the court with her and, yeah, it was even better to beat her and play my game tonight and really stay very solid with my game - so this was very, very good day today."

Svitolina saved five of the six break points she faced in the match, as she dropped serve just once when she attempted to secure the bagel in the opening set. The No.5 seed won an identical 61 percent of the points played on her serve and on return, as she converted on six of the seven break points she created.

"I was expecting that she would put pressure on my serve and that's the way she's playing," Svitolina assessed. "I was just trying to stay really focused and on the things that I can control. You know, to prepare my serve to be ready for next shot straight away, because she turns very quickly.

"I was very happy that I could really stay like that during all the match and didn't do so many unforced errors. It was quite solid performance for me."

With the momentum firmly in her corner, Svitolina snuffed out Williams' lone chance to get into the match back on serve in the second set, as she saved a break point in the fourth game after taking the lead in the first game of set two.

"That game was very important. I knew it, and that's why I was extremely focused on my serve, on my second shot as well," Svitolina said. "If you give her small opportunity, she can get back into the game and then it's equal for everyone. It was extremely important to serve well and then put pressure on her and to don't do unforced errors on easy shots.

"I think my level now is much, much better, so I can handle this. Of course, at some point I can miss, but most of the points I think are much better now. I can handle it better."