PARIS, France -- Elina Svitolina of Ukraine emerged victorious in a first-round battle between marquee names at Roland Garros on Sunday, as the No.9 seed ousted former World No.1 and 2002 finalist Venus Williams of the United States, 6-3, 6-3.

"I was just trying to focus on things that I can control," Svitolina told the media, after her win. "There's nothing more that I was thinking about. I know it was not easy. But for me, it was just the motivation for me to get straight into the tournament, to have a mindset straight on. You know, I had no time to lose from the first point.

"And I think Venus is sometimes playing unbelievable, and I had to accept and move forward. So that's why it got me straight into fighting mindset, and I think helped me today to go through this match."

Photos: Roland Garros 2019: The 32 seeds and their best French Open performance

World No.9 Svitolina, a two-time Roland Garros quarterfinalist, had been struggling with injury during the clay-court season and had gone just 0-2 on the surface coming into Paris, including a loss to Victoria Azarenka in her first match at Rome, where Svitolina was the two-time defending champion.

However, the Ukrainian looked solid and serene in her one-hour and 13-minute victory over seven-time Grand Slam champion Venus Williams, who is currently ranked World No.52. Svitolina finished the match with 16 winners, one more than Williams, and the American's 34 unforced errors well outpaced Svitolina's 15. Svitolina also won a stunning 63 percent of points off of the Williams serve.

"It's important to keep low expectations because since with injuries is tricky," Svitolina stated. "You can feel good and then sometimes it can, you know, just pop up. And it's important just to take one match at a time, to do everything what is in your power, and what you can control is your recovery. And then, if it's not meant to be, it's like that. But it's important to just keep focus."

Svitolina queued up an all-Ukrainian affair in the second round, as she will next face her compatriot Kateryna Kozlova. Kozlova eliminated American qualifier Bernarda Pera, 6-2, 7-6(5), in another opening-round clash earlier on Sunday. Svitolina won their only previous meeting, on home soil in 2013.

"I know Kateryna for a long time," said Svitolina. "I haven't seen much of her game recently, but we'll see how it goes. I just try not to think so much about the opponents who is on the other side of the net. I just try to take one match and just be ready for it. For me, the most important is that I am ready; I am feeling good on court; my movement is good; I'm mentally fresh, and that's what matters."

The opening set started with a number of grueling rallies, as the combatants attacked each other with crosscourt angles, trying to jump all over their opponent’s service games. After a pair of routine holds to start the encounter, five consecutive service breaks followed, including the last two of those at love. When the dust settled after that run of breaks, Svitolina led 4-3.

The Ukrainian finally quelled that streak with a service hold for 5-3, as the Williams unforced errors mounted off the forehand side. The American was unable to rebound as she served to stay in the set; despite evading the forehand, Williams fired a double fault and two backhand miscues to drop serve at love once more, ceding the set to the No.9 seed.

Williams won only 10 of 28 points on her vaunted service in the first set, but she was more effective as the second set began, saving two break points to pull through a difficult service game and crack open a 3-1 lead.

Svitolina, however, would not remain behind for long. The No.9 seed used two stirring backhands, at the beginning and the end of the game, to cobble together a service break and get back level at 3-3. Another break would soon follow, as the Ukrainian’s creative passing shots helped her to a 5-3 lead and put her one game away from victory.

Williams fended off two match points in the following game, the second with a vintage screaming crosscourt forehand winner. But a strong serve by Svitolina set up match point number three, and there, a wide service return by Williams ended the encounter between two of the WTA’s most famous names.