However, the Spaniard was faster off the blocks as she dismissed Johanna Larsson in only 64 minutes, asserting her authority in the longer rallies.
Muguruza is bidding to reach the second week at Roland Garros for the sixth straight year but faces a tricky opponent in the ninth-ranked Svitolina, who is much fresher having received a walkover in the previous round when compatriot Kateryna Kozlova was ill.
"Personally, it's the type of matches that I want to play," Muguruza said of a potentially touch test early on.
"It can be, you know, any deep-round match, but it's in the third round. I'm highly motivated because she's one of the top players right now."
The pair last met at Roland Garros in the 2012 qualifying rounds, with Muguruza recording a comfortable victory.
"(2012) was a very long time ago. So I think now it's different, and I could watch more and pay attention to our last matches rather than those 2012 qualies," Muguruza said.
"Last time we played was in Dubai... We played excellent matches, long rallies, and very different matches. It's going to be interesting."
In the men's draw, defending champion Rafa Nadal will look to continue his smooth progress against Belgian David Goffin, while Roger Federer takes on Norwegian youngster Casper Ruud.
(Reporting by Hardik Vyas in Bengaluru; Editing by Toby Davis)
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