A month after she was knocked out of the Madrid Open in straight sets by the Hungarian, Ukrainian seventh seed Svitolina could not find her range on the Suzanne Lenglen Court, falling apart in the opening set after cancelling out an early break.
Svitolina, however, bounced back in the second but it was not as easy as the 6-1 scoreline suggested.
The 31-year-old fell 3-1 behind in the decider but clawed her way back and broke decisively for 4-3. Serving for the match at 5-4, she was broken to love, losing eight points in a row to find herself trailing 6-5.
She held serve to force a super tiebreak, during which her opponent eventually unravelled.
"Definitely the support of you guys has been unbelievable, this kind of battle is never easy. It was an amazing match, I'm pleased with my performance," said Rome champion Svitolina, who has now played four consecutive three-set matches.
"A first round like this puts you right on track. Mental strength took me over the line, as well as my physical condition."
There were no such problems for another fancied contender, Australian Open champion and second seed Elena Rybakina, who cruised past Slovenia's Veronika Erjavec 6-2 6-2. The Kazakh will play Yuliia Starodubtseva in the second round.
In one of the upsets of the day, Colombia's Camila Osorio stunned Russian 14th seed Ekaterina Alexandrova 6-2 6-4 to set up a second-round clash with Kazakhstan's Yulia Putintseva.
American sixth seed Amanda Anisimova eased past French wildcard Tiantsoa Rakotomanga Rajaonah 6-3 6-1 and will now face Austria's Julia Grabher. Former finalist and Italian 13th seed Jasmine Paolini beat Dayana Yastremska 7-5 6-3.
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