Puig won 6-3, 3-6 and 6-2 over Vinci in an hour and 50 minutes while the 32-year-old Argentinian made a 7-5, 6-3 and 6-4 over Mannarino, reports Efe.
Puig's next opponent is set to be the winner of the match between US's Louisa Chirico and Latvian Jelena Ostapenko, and Zeballos will play against the winner of the match between Croatian Ivo Karlovic and Greek Stefanos Tsitsipas.
In another match, Switzerland's Timea Bacsinszky defeated Sara Sorribes, who became the first Spanish woman to lose to the Swiss tennis player in the French Open.
Bacsinszky reached French Open round two after winning 6-1 and 6-2 over Sorribes in an hour and 22 minutes.
Bacsinszky, the 30th seed, is set to face in round two the winner of the match between United States Madison Brengle and Germany's Julia Gorges.
(This story has not been edited by Social News XYZ staff and is auto-generated from a syndicated feed.)
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