STRASBOURG, France -- No.5 seed Elena Rybakina of Kazakhstan slid into the quarterfinals of the Internationaux de Strasbourg on Tuesday, fighting through a closely-contested second set before ousting 2013 champion Alizé Cornet of France, 6-3, 7-6(8).

After a hot start to the year, where she won the title in Hobart and reached three other finals, World No.18 Rybakina had yet to reach a quarterfinal in her first three events since the resumption of tournament play. But Rybakina found her way back into that round this week, moving into the elite eight with her win over homeland hope Cornet.

"I was just focusing on every point, because it’s not the first time I’m actually up [in the score]," Rybakina told the press, after the match. "Last tournament in Rome, I was up, for example, and my concentration went down. I just knew that I had to focus on every point. It doesn’t matter, the score, just work every point and try to do my best."

Still, it took a lot of effort to attain Tuesday's win, as Rybakina held match points at 5-3 and 5-4 in the second set before Cornet charged back. Cornet ended up holding two set points in the second set, one at 6-5 and one in the tiebreak, before Rybakina was able to fight her way back from 2-5 down in the breaker to garner the straight-set victory.

"[Cornet] played really good from 4-2," said Rybakina, referring to the second-set fightback by the Frenchwoman. "She was defending every point, she was fighting until the end, so it was not easy, of course."

Thus, Rybakina improved her head-to-head record against World No.52 Cornet to 2-0 with her one-hour and 49-minute victory. The 21-year-old had ousted Cornet in the second round en route to her Hobart title earlier this season, which was the second of the rising Kazakh’s two WTA singles crowns in her career.

In the quarterfinals, Rybakina will face either former Top 25 player Zhang Shuai of China or French teenager Clara Burel, who will meet each other in Tuesday’s last singles encounter.

"I have to think about the tactics, and focus on my serve," said Rybakina, looking forward to the next round. "Today, in the beginning of the match, it was good, the serve, but then I dropped a bit, doing many double faults in the second set. So I’ll focus on serve, and we’ll see how it goes."

The powerful hitting by Rybakina was present from the very start of the affair, and the Kazakh had initial chances at 2-1 when a backhand crosscourt winner gave her two break points. However, Cornet saved the pair, with the second being erased with a lob winner after chasing down a dropshot, and the home hope held on for 2-2.

Rybakina, though, kept on firing, using her forehand wing to earn two more break points at 3-2. Cornet boldly saved the first in that game with a backhand winner, but on the next point, a forehand by the Frenchwoman flew wide, and Rybakina had claimed the first service break of the match.

The depth and defense by Cornet allowed her to come out on top in some exquisite rallies during the opening frame, but she was unable to work her way into the Rybakina service games, as the Kazakh never faced a break point in the set. At 5-3, an overhead winner gave Rybakina triple set point, and she only needed one, clinching the set with an error-forcing backhand.

Cornet double faulted to drop serve in the opening game of the second set, but the Frenchwoman at last clinched a break in the following game to get level at 1-1. Nevertheless, Rybakina broke again for 2-1, sealing that game with a backhand winner down the line, then staved off two break points to stop the run of breaks and hold on for a commanding 3-1 lead.

At 4-3, Rybakina erased another break point with a big serve, and held on for 5-3. The Kazakh was rewarded in the next game, as she pulled a 40-0 lead for Cornet to deuce, then earned her first match point with a return winner off the netcord. Cornet was able to extricate herself from that situation and hold for 5-4, but faced two additional match points in the next game.

Cornet, though, used deft play to get out of that jam as well, and she suddenly found a break point with a forehand winner. On that chance, the Frenchwoman used a backhand pass to convert the break point, and Cornet had pulled back to 5-5.

The unseeded player was on a roll, and garnered a set point at 6-5 after a long backhand by Rybakina. The Kazakh, though, fired a forehand winner to pull back to deuce, and after a backhand winner to hold, the pair was all queued up for a tiebreak.

It was Cornet who cracked multiple groundstroke winners in the early stages of the breaker, and a crosscourt backhand gave the Frenchwoman a sturdy 5-2 lead, putting her again within touching distance of a third set. However, Rybakina blasted big returns in the next two points to wipe out the two mini-breaks, and after another big serve, it was all square at 5-5.

There were no more mini-breaks up to 8-8, as two more match points for Rybakina and another set point for Cornet came and went. Finally, a backhand winner down the line let Rybakina claim a point on Cornet’s serve, which gave the fifth seed a 9-8 lead and a sixth match point. There, a good serve was returned long, and Rybakina had squeaked out the second set, and the win.

2020 Strasbourg highlights: Rybakina slides past Cornet