PARIS, France - No.4 seed Elina Svitolina survived an early scare in the first round of the French Open on Sunday before taking out unseeded Australian Ajla Tomljanovic, 7-5, 6-3.

One of the prohibative tournament favorites entering the action in Paris, Svitolina trailed 5-1 in the opening set and faced set point, but turned things around from there to move safely through to the second round in one hour and 29 minutes.

The Internazionali BNL d'Italia champion won the next eight games with her back against the wall, eventually earning victory in the match by winning 12 of the last 15 games overall. 

"I found myself, and I was fighting to get back into the match," Svitolina said. "I think for me it was very important to play an extra ball over the net, and then to fight until the end, until the last point of the first set, to find my game, and this was the key.

"I think I did it pretty good, and then my level was getting better and better. It's probably a mixture of things. She was striking the ball well. I was a little bit off, sometimes going for too much. I just tried to find my way into the match...I was trying, you know, to build my game, and I think in the end it was good for the first round."

Tomljanovic was looking for her second career win at the French Open against a Top 10 player, having defeated No.3 seed Agnieszka Radwanska en route to her best-ever Grand Slam showing: the fourth round in 2014.

After building an early lead, Tomljanovic started to struggle on serve, opening the door for the No.4 seed on return.

The World No.68 served three of her five double faults in the opening set in a lengthy eighth game, including one on her lone set point, to drop serve for the first time in the match. 

Given second life, Svitolina duly wrestled the momenum away from Tomljanovic, and held easily to force the Aussie to serve for the opener once more. This time, the 25-year-old would not even hold set point, and Svitolina found herself not only back on level terms, but ahead for the first time since she held in the first game of the match a short time later.

The Ukrainian cleaned up her tennis in the second set after hitting 12 winners to 19 unforced errors over the first 12 games, recording 10 winners to just seven unforced. She also went 5-for-11 on break points she created in the match.

With the victory, last year's quarterfinalist will next face the winner of the first round match between 2010 champion Francesca Schiavone and Slovakia's Viktoria Kuzmova.

Svitolina and Tomljanovic shake hands at the net. (©Jimmie48/WTA)

With her second round match not slated to take place until Wednesday, the World No.4 joked with the press afterwards about how she'd spend her time until then. 

"I'll go home and come back (laughter.) I want to prevent doing this again next match, so that's why I'm going to go back on court in 10 minutes and work on my game," Svitolina said. 

"I know that I have to put lots of hours on court to get better and for me there is only way to get better is to practice - to get better, to improve my game each day, each match. I have to stay really focused, and it's good I'm going to have a couple days off and physically I can be ready for next match."