Cilic will take on Nick Kyrgios in Sunday’s final after the Australian eased past Czech second seed Tomas Berdych 6-4 6-2 in the other semi-final.
Kyrgios relied on a strong first serve, firing 15 aces to prevail against Berdych.
While Cilic conceded eight points on his service games in a one-sided first set against Paire, the Frenchman's first-serve percentage was only 33.
Paire rediscovered his touch in the second set and Cilic lost focus in the tiebreak as the match went into a decider.
The former U.S. Open champion, however, regained his composure to break for 4-2 in the third set before wrapping up the victory on his first match point.
(Writing by Julien Pretot in Paris; editing by Clare Fallon)
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