Nineteen of the Russian's twenty-one championships have been won on hard courts
A resurgent the Russian player claimed his initial title for 882 days with victory over Frenchman Moutet in the tournament championship match.
The Russian, a former world number one, has experienced a difficult year, managing just one match at the Grand Slams and experiencing a setback at the US Open.
The player's inconsistency on the professional circuit - and issues with his serve in particular - resulted in him exiting of the world's top 10 and finally splitting with long-term mentor his previous coach.
Presently training with Thomas Johansson and Rohan Goetzke, Medvedev has gradually improved in the last few weeks - culminating in a closely contested 7-5 4-6 6-3 triumph over opponent Moutet.
This marks the player's initial championship after the 2023 Rome Masters and first on a hardcourt since that period of 2023.
The win also signifies he has won 21 victories at twenty-one distinct competitions.
"For the first time I have attended a tournament with my children simultaneously, so to get a trophy is particularly special," commented world number 14 Medvedev.
"This title is in honour of my child her name, because the initial championship I achieved when my first daughter her name was born was for her."
The tennis star, the former major winner, had been defeated in his last six finals, comprising in the German tournament previously this season.
Medvedev's retrieving approach and recurring reactions on court had caused commentators to wonder if his skill to compete at the elite level was finished.
However the 29-year-old has made changes in the last few weeks, striving to approach the net and play assertively, supported by an improved serving game.
Medvedev recovered from a disadvantage in the opening set against the difficult opponent, securing 4 of the last five games to take the lead.
Both players exchanged service breaks in the second set before Moutet, striving for his initial ATP Tour title, gained dominance to create a decider.
Moutet rescued four early-game opportunities in a competitive deciding set before Medvedev broke to that score to close out the victory.
Suitably, Medvedev earned victory with a rally at the net area, with his opponent failing to handle a shot after two hours and 38 minutes.