The top seeded world number 10 appeared to be suffering from abdominal pains and went 3-0 down in the opening set before prevailing.
He wrapped up with his first match point when Mathieu sent a backhand just long.
"(Mathieu) hit the ball hard, at the beginning I could not compete but then I served much better," said Gasquet, now a four times winner in Montpellier after titles in 2006, 13 and 15.
(Reporting by Julien Pretot, editing by Alan Baldwin)
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