Round Up: Elina Svitolina beats Ajla Tomljanovic to become first big name through

Ukraine's Elina Svitolina overcame a slow start to power past Australia's Ajla Tomljanovic 7-5 6-3 and become the first big name to reach the second round of the French Open on Sunday.

Elina Svitolina of Ukraine plays a forehand during her ladies singles first round match against Ajla Tomljanovic of Australia during day one of the 2018 French Open at Roland Garros on May 27, 2018 in Paris, France.

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Ukraine's Elina Svitolina overcame a slow start to power past Australia's Ajla Tomljanovic 7-5 6-3 and become the first big name to reach the second round of the French Open on Sunday.

Under beautiful blue skies in the French capital, the fourth seed was broken twice early in the opening set before clawing her way back into the match from 5-1 down, by pinning her opponent behind the baseline and testing the Australian's backhand as she rediscovered her groundstrokes.

The Ukrainian wrapped up the match with a comfortable second set, to stretch her head-to-head lead over Tomljanovic to 3-0.

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"It was not an easy start and I had to really wake up. I had to step up my game," Svitolina said straight after the match.

Svitolina arrived in Paris as one of six players with a chance of ending the tournament as World No. 1, and had not failed to make it to the second round of a Grand Slam since the U.S. Open in 2014.

The 23-year-old struggled to find her rhythm early on until the eight game when a Tomljanovic double fault handed Svitolina a second break point of the game. The Australian then hit long to make it 5-3 and Svitolina launched her comeback.

Tomljanovic lost the opening set with a cautious second serve that was dispatched by Svitolina, the Australian slamming her racket into the clay in an outburst of frustration after surrendering a four-game lead.

Svitolina dictated the second set, spreading the ball across the baseline and offering up some deft drop shots that stretched her opponent.

At 3-4 down in the second, Tomljanovic smacked a double-handed backhand into the net to hand Svitolina a break point, which she won easily before closing out the set.

Svitolina will next face either 2010 champion Francesca Schiavone -- here this year as a qualifier -- or Viktoria Kuzmova, who play later on Sunday.

Sloane Stephens enjoyed her first Grand Slam win as the reigning U.S. Open champion by demoslishing Dutchwoman Arantxa Rus 6-2 6-0 in the first round of the French Open on Sunday.

The American 10th seed's first major as a Grand Slam winner lasted only three sets after she was beaten in the first-round of the Australian Open.

That result in January was one of eight successive defeats she suffered following her Flushing Meadows triumph last September.

But if Rus harboured any hopes of pulling off another upset, those hopes were dashed in 49 brutal minutes by Stephens.

The Dutwoman managed to produce only two winners during the contest as Stephens ran her ragged from the baseline with a non-stop flow of flying groundstrokes.

She wrapped up the win to secure a second round match with either Russian Ekaterina Alexandrova or Magdalena Frech from Poland.

France's Alize Cornet recovered from a set down to defeat Italian Sara Errani 2-6 6-2 6-3 in a show of powerful baseline hitting on Sunday to progress to the second round of the French Open.

Cornet struggled to find her forehand range in the first set, at one point venting her frustration at a ball boy and drawing boos from the crowd, before she began to dictate the match from the back of the court with her powerful backhand.