The Ukrainian, number six in the world but leading the race rankings of results accumulated during 2017, struggled early on as her heavy groundstrokes fell short or wide.
Pironkova took advantage, reeling off four games in a row to take the first set.
In a match littered with 54 unforced errors that the players shared almost equally, fifth seed Svitolina then started to find her range and struck back.
She took the second set when her 77th-ranked opponent drove a halfcourt backhand into the net, and did enough to stay on top in the third.
(Editing by John Stonestreet)
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