Nineteen of Medvedev's 21 titles have been achieved on hard surfaces
A resurgent Medvedev claimed his maiden title for 882 days with victory over Frenchman Moutet in the tournament championship match.
The Russian, a ex- number one, has endured a torrid season, managing just a single victory at the Grand Slams and undergoing a difficult moment at the New York tournament.
Medvedev's varied form on the tennis tour - and difficulties with his serving in particular - resulted in him falling of the top ten and finally parting ways with long-time mentor his previous coach.
Presently training with his coach and Rohan Goetzke, he has gradually improved in the recent weeks - peaking in a closely contested three-set triumph over opponent Corentin Moutet.
It is Medvedev's maiden trophy since the Italian tournament and initial on a hard court since spring of the previous year.
The win also indicates the Russian has secured 21 titles at twenty-one different tournaments.
"For the first time I'm at a competition with my two daughters simultaneously, so to win a championship is particularly special," stated world number 14 Medvedev.
"This title is in dedication of my younger daughter her name, because the initial championship I got when my older daughter my daughter was born was for her."
The tennis star, the past champion, had lost his previous six title deciders, including in that event earlier this year.
Medvedev's retrieving strategy and regular reactions on the tennis court had prompted some to doubt if his capacity to perform at the top level was over.
Yet the player has implemented adjustments in recent weeks, making an effort to advance forward and perform positively, supported by an better service.
Medvedev came back from a deficit in the initial set against the tricky opponent, winning 4 of the last five points to gain the advantage.
Both players traded breaks in the middle set before the Frenchman, bidding for his initial tour title, seized the initiative to force a final set.
Moutet saved 4 early-game chances in a competitive third set before the Russian secured a break to 15 to serve for the match.
Appropriately, he earned the win with a rally at the net area, with his opponent failing to control a volley after two hours and 38 minutes.