19 of Medvedev's 21 championships have been achieved on hard courts
A comeback Medvedev claimed his first trophy for 882 days with a win over Frenchman Moutet in the Almaty Open championship match.
The athlete, a ex- world number one, has experienced a challenging period, winning just one match at the major tournaments and undergoing a difficult moment at the American major.
Medvedev's inconsistency on the tennis tour - and issues with his serving in especial - resulted in him falling of the top ten and eventually separating with former mentor his previous coach.
Presently training with Thomas Johansson and Rohan Goetzke, Medvedev has gradually advanced in the past month - culminating in a hard-fought 7-5 4-6 6-3 victory over challenger Corentin Moutet.
It is his maiden trophy following the 2023 Rome Masters and first on a hard surface from that period of the previous year.
Victory also means Medvedev has won twenty-one titles at twenty-one various tournaments.
"This marks the first occasion I have attended a competition with my children at once, so to win a trophy is particularly special," commented world number 14 Medvedev.
"This championship is in dedication of my younger daughter Victoria, because the first title I got when my older daughter her name was delivered was for her."
Medvedev, the 2021 US Open champion, had lost his last six finals, featuring in Halle previously this season.
His retrieving strategy and frequent outbursts on the playing surface had caused observers to doubt if his ability to play at the highest level was over.
Yet the 29-year-old has implemented adjustments in recent weeks, making an effort to approach the net and compete positively, supported by an enhanced serve.
Medvedev came back from a disadvantage in the opening set against the challenging opponent, securing four of the concluding five games to gain the advantage.
The competitors exchanged breaks in the second set before the challenger, striving for his initial ATP Tour championship, took control to push for a third set.
He saved four early break points in a close third set before the Russian secured a break to 15 to serve for the match.
Fittingly, Medvedev earned victory with a shot at the net area, with his opponent unable to handle a return after two hours and 38 minutes.