Medvedev, victor at the US Open in 2021, had previously suffered defeats in his last half-dozen title matches, including one in Halle earlier this year.
His defensive approach and regular displays of temper on the court had raised questions about whether he could continue to compete at the highest level.
However, the 29-year-old has recently implemented adjustments, actively trying to approach the net and adopt an aggressive playing style, supported by a more effective serve.
He recovered from an initial setback in the first set against the challenging Moutet, securing victory in four of the last five games to gain the advantage.
Both players exchanged breaks of serve in the second set before Moutet, aiming for his inaugural ATP Tour title, seized control to extend the match to a deciding set.
Moutet thwarted four break point opportunities early in a closely contested third set before Medvedev finally broke serve, setting himself up to serve for the match.
Appropriately, Medvedev clinched the win with a point executed at the net, as Moutet failed to manage a volley after two hours and 38 minutes of play.
