Basilashvili, world No. 74, needed one hour and 59 minutes to beat Baldi, world No. 370, reports Efe.
Basilashvili, 26, is set to play the second round against Serbia's Novak Djokovic, a former world No. 1 and four-time champion at the Italian Open.
This is to be Basilashvili's first time facing the 2017 Italian Open finalist.
Currently world No. 18, Djokovic thrashed Ukraine's Alexandr Dolgopolov, world No. 54, in the first round 6-1, 6-3.
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