The players exchanged a break of serve in the opening set, but it was 19-year-old Zverev who gained the upper hand in the tie-break.
By forcing Zverev to hit several forehand errors, Gasquet managed to get the service break back later in the set for 2-all.
Grigor Dimitrov won his second title of the season by beating David Goffin 7-5 6-4 in the final of the Sofia Open in Bulgaria. Zverev would later team up with brother Mischa to win the doubles title, becoming the first player since Lleyton Hewitt in 2014 to win the singles and doubles at the same event.
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Alexander Zverev won his second career ATP Tour title with a 7-6 (4), 6-3 win over three-time defending champion Richard Gasquet in the finals of the Open Sud de France.
Gasquet faced two break points while serving down 3-4.
"It was a hard match", said Gasquet. "It was close during the first set".
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The third-seeded Gasquet needed two hours, 16 minutes to finish off De Schepper and move closer to his bid for a third straight tournament title.
Defeat ended world number 22 Gasquet's 10-match winning streak in Montpellier.
"I'm very happy to win my first title of the year", said Zverev. "The recipe for my success here will be revealed when I retire [laughing], but for sure I'll come back here next year".
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Krajicek said the presence of highly-rated German teenager Zverev and Bulgarian Dimitrov was a stroke of fortune.