The former world number one from Japan needed a deciding set to beat Lucia Bronzetti in the opening match on Court Philippe Chatrier.
However, when the Italian slashed a backhand into the net, Osaka had the break at the end of the decider and served out for a 6-1 4-6 7-5 victory.
Osaka famously avoids looking at her potential draw at tournaments, but it was difficult to avoid finding out she has a likely match-up with current world number one and three-time winner Iga Swiatek next.
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