Local favourite Gasquet, bidding for a fourth title overall at the indoor event, dropped the firset set on the tiebreak and was broken twice in the second as the 19-year-old Zverev claimed his second career title.
Defeat ended world number 22 Gasquet's 10-match winning streak in Montpellier.
Zverev, who will compete in the doubles final later on Sunday alongside his brother Mischa, had beaten much-fancied second seed Jo-Wilfried Tsonga in his semi final.
Gasquet saw off compatriot Benoit Paire to reach the final. (Reporting by Ed Dove)
Read the original article on Eurosport: Zverev denies Gasquet Montpellier hat-trick