19 of Medvedev's twenty-one titles have been won on hardcourt
A resurgent the Russian player won his maiden title for nearly 30 months with victory over Frenchman Moutet in the competition final.
Medvedev, a ex- number one, has endured a challenging season, managing just one match at the Grand Slams and suffering a difficult moment at the American major.
The player's unpredictability on the professional circuit - and struggles with his serve in particular - caused him falling of the top ten and finally separating with former mentor Cervara.
Now training with Thomas Johansson and his other coach, Medvedev has gradually progressed in the past month - climaxing in a hard-fought competitive win over opponent Moutet.
It is his first title following the 2023 Rome Masters and initial on a hardcourt after that period of the previous year.
Success also means Medvedev has won 21 victories at 21 distinct events.
"For the first time I am participating in a event with my two daughters together, so to get a trophy is particularly special," commented world number 14 the champion.
"This title is in tribute of my younger daughter Victoria, because the initial championship I won when my child her name was born was for her."
The tennis star, the 2021 US Open champion, had lost his last six title deciders, comprising in the German tournament previously this season.
The player's counter-punching strategy and regular emotional displays on the tennis court had caused some to doubt if his skill to compete at the elite level was concluded.
Yet the player has altered his approach in the last few weeks, striving to advance forward and perform positively, supported by an improved serve.
The champion fought back from a break down in the opening set against the tricky opponent, securing 4 of the concluding five exchanges to go ahead.
The competitors exchanged breaks in the middle set before the Frenchman, attempting for his first tour victory, took control to create a final set.
The opponent rescued 4 early-game opportunities in a competitive deciding set before the Russian won the break to that score to close out the victory.
Fittingly, the winner secured the win with a point at the net, with Moutet failing to handle a shot after a lengthy match.