Nineteen of Medvedev's 21 victories have been won on hard surfaces
A resurgent the Russian player claimed his first title for nearly 30 months with a win over Frenchman Moutet in the competition final.
The Russian, a former world number one, has had a difficult year, achieving just a single victory at the big events and suffering a setback at the New York tournament.
Medvedev's inconsistency on the professional circuit - and struggles with his serve in particular - led to him falling of the world's top 10 and finally splitting with long-time mentor Gilles Cervara.
Presently collaborating with his coach and his other coach, he has gradually advanced in the past month - culminating in a hard-fought 7-5 4-6 6-3 triumph over challenger Moutet.
This represents the player's initial title after the 2023 Rome Masters and first on a hard court from that period of that year.
The win also signifies the Russian has achieved 21 victories at twenty-one various tournaments.
"This marks the first occasion I have attended a tournament with my two daughters at once, so to win a trophy is especially meaningful," said tennis professional the champion.
"This victory is in tribute of my child Victoria, because the initial championship I achieved when my first daughter my daughter was born was for her."
The tennis star, the 2021 US Open champion, had been defeated in his past six championship matches, featuring in that event previously this season.
Medvedev's counter-punching play style and frequent emotional displays on court had led some to wonder if his capacity to compete at the top level was finished.
However the 29-year-old has made changes in the past month, making an effort to approach the net and play aggressively, backed up by an improved serving game.
The champion recovered from a deficit in the first set against the difficult Frenchman, winning four of the last five exchanges to take the lead.
The pair traded break points in the following set before the challenger, attempting for his initial ATP Tour title, gained dominance to push for a decider.
The opponent defended four early-game break points in a competitive third set before Medvedev broke to 15 to secure the win.
Appropriately, Medvedev earned the title with a point at the net, with Moutet failing to handle a shot after a lengthy match.