PARIS, France -- No.28 seed Maria Sharapova of Russia moved into the third round at the French Open for the 13th time in her career following a hard-fought 7-5, 6-4 second-round victory over Croatian Donna Vekic on Thursday.

The 2012 and 2014 French Open champion emerged victorious in her first meeting with Vekic after two tough sets which took nearly two hours. Sharapova was 6-for-6 at the net and won more than half of points while returning.

"There were definitely ups and downs," Sharapova said to the press, after the match, "Maybe that's a result of not knowing each other's games very well, and playing on a little bit of a different court that I felt maybe played a little bit differently than [Court] Suzanne Lenglen."

"You just kind of feel a different rhythm on a different court," Sharapova continued. "It took a little bit of time for me to adjust to that, more so today than maybe other days. But overall, I mean, in the moments when I needed to come through, I did."

"I think you always have to feel that you're improving and there are things that you're working on, because that will always make you better," Sharapova added. "There are a lot of things I feel I could have done better since the last two matches, and I hope I will have to."

In the third round, Sharapova will take on No.6 seed Karolina Pliskova of the Czech Republic in an intriguing encounter. Pliskova, a former World No.1 like Sharapova, overcame her compatriot, 2015 French Open runner-up Lucie Safarova, in three sets in the second round on Thursday.

"I don't expect extremely long rallies against an opponent like [Pliskova]," said Sharapova. "But sometimes it's not what it takes to win a match, and I think you have to kind of take care of your service games, and I have to serve better than I have been and take care of the return."

"But that side of the game, I feel, has improved in the last few months, and I like the challenge of coming up against a really good server."

Vekic got off to a strong start, breaking Sharapova in the opening game of the match, but Sharapova immediately broke back for 1-1 as the two power hitters felt each other out in the opening stages. The combatants were separated by very little as they reached 3-3, closing out games with blistering forehands.

Sharapova squeaked ahead, breaking Vekic for a 5-3 lead after the Croatian dropped serve with two unforced errors and a double fault. But Sharapova was unable to serve out the set at that juncture, as Vekic got back on serve with a strong service return forcing an error into the net.

At 5-4, Vekic fended off Sharapova’s first set point with a forehand winner, and finally held for 5-5 on her fifth game point. Sharapova quickly held serve at love to lead 6-5, closing out that game with a backhand winner and putting the pressure swiftly back on Vekic.

Vekic started the game with a double fault, and although the Croatian recovered to reach game point, a second double fault there brought the game back to deuce. On the following point, Sharapova slammed a forehand winner to reach set point for the second time, and this instance was converted after Vekic hit a forehand miscue into the net.

After an early exchange of breaks in the second set, Sharapova claimed what appeared to be the pivotal break of the match, jumping ahead 3-1 when a sturdy backhand off the Russian’s racquet was volleyed into the net by Vekic. Sharapova moved through her next two service games with ease, reaching 5-2 and putting Vekic in dire straits.

But Vekic survived a difficult service game, holding for 5-3 from deuce via two powerful serves. Sharapova had the chance to serve out the match there, but the Russian faltered, sending a forehand wide on Vekic’s second break point of the game and allowing the Croatian to work her way back on serve at 5-4.

The following game was a barnburner, as Vekic staved off four match points in a valiant attempt to stay alive. The two players used every inch of court in their attempts to eke out the game, as every time Sharapova clutched a lead with a brilliant forehand or a wily drop shot, Vekic would reply with a solid serve or stunning backhand.

But Sharapova reached a fifth match point in that game with a forehand winner down the line, and in this instance, Vekic could not escape. On the subsequent point, the Russian boomed a forehand service return past Vekic for a clean winner, sealing victory after two protracted sets.