The 32-year-old Pole, ranked world No. 63 by the Women's Tennis Association (WTA), overcame the 61st-ranked Croat 6-3, 6-4 in their first-round encounter on Monday.
Linette will next play Ukraine's Dayana Yastremska for a place in the last 16.
In 2022, Linette reached the women’s singles quarterfinals and won the doubles title at the Charleston Open partnering with Slovenia's Andreja Klepač.
"I'm glad I'm back here," Linette said on Monday. "There's no better way to start the clay season than with a victory," she added.
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Source: IAR, PAP