Thiem, seeded third, failed to serve out the opening set at 5-4 but won the final three points in the tiebreak, before taking control of the match in the second set.
The 24-year-old Austrian finished with 19 aces and converted three break points to collect his 36th match win of the season.
Nadal returns to number one before Wimbledon
Thiem is set to make his fifth consecutive appearance at Wimbledon next month but has never got beyond the fourth round.
However, he will be looking to improve that record on the back of his maiden Grand Slam final appearance at Roland Garros.
Thiem will next face Japan's Yuichi Sugita, who beat German wildcard Maximilian Marterer 6-4 5-7 6-3.
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