Nineteen of the Russian's 21 championships have been achieved on hard courts
A comeback the Russian player won his maiden championship for 882 days with a win over Frenchman Moutet in the tournament title decider.
Medvedev, a former world number one, has had a difficult season, achieving just a single victory at the big events and experiencing a meltdown at the New York tournament.
His unpredictability on the ATP Tour - and difficulties with his serve in particular - resulted in him exiting of the elite rankings and eventually parting ways with long-term mentor Cervara.
Presently working with Thomas Johansson and his other coach, he has consistently improved in the recent weeks - culminating in a tightly fought 7-5 4-6 6-3 triumph over Frenchman Moutet.
It is the player's maiden championship after the 2023 Rome Masters and first on a hardcourt after March of that year.
The win also means Medvedev has won twenty-one titles at twenty-one different competitions.
"For the first time I am participating in a tournament with my both daughters together, so to secure a title is particularly special," commented tennis professional Medvedev.
"This championship is in dedication of my child my daughter, because the first title I got when my child her name was born was for her."
The tennis star, the former major winner, had failed in his last six championship matches, featuring in the German tournament earlier this year.
Medvedev's defensive approach and frequent emotional displays on court had caused observers to wonder if his skill to perform at the elite level was over.
Yet the athlete has altered his approach in recent weeks, making an effort to come to the net and compete aggressively, backed up by an improved serving game.
Medvedev recovered from a deficit in the initial set against the tricky Frenchman, taking 4 of the final five points to gain the advantage.
The competitors exchanged break points in the following set before Moutet, striving for his initial tour title, took control to create a third set.
The opponent saved 4 early-game opportunities in a tight deciding set before the Russian secured a break to that score to close out the victory.
Fittingly, Medvedev earned victory with a rally at the front of the court, with the Frenchman incapable to manage a volley after two hours and 38 minutes.