The fourth seed lost control at times on Court Suzanne Lenglen, but his bludgeoning forehand made the difference as he set up a meeting with local favourite Gael Monfils.
Monfils had no trouble seeing off fellow Frenchman Antoine Hoang, whose wild-card run came to an end in a 6-3 6-2 6-3 defeat on Court Philippe Chatrier.
Thiem's opponent, world number 47 and claycourt expert Cuevas, was a tougher nut to crack but it was a matter of when, not if, for the Austrian.
(This story corrects Cuevas's first name)
(Reporting by Julien Pretot; Editing by Tony Lawrence)
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