19 of Medvedev's 21 titles have been won on hard surfaces
A resurgent the Russian player won his first trophy for nearly 30 months with a win over opponent Moutet in the Almaty Open title decider.
The athlete, a ex- number one, has experienced a difficult season, managing just one match at the Grand Slams and experiencing a meltdown at the New York tournament.
The player's unpredictability on the ATP Tour - and issues with his service game in especial - resulted in him exiting of the top ten and eventually separating with long-term trainer Gilles Cervara.
Now training with his coach and Rohan Goetzke, he has gradually advanced in the recent weeks - climaxing in a tightly fought 7-5 4-6 6-3 victory over Frenchman Moutet.
It is his first trophy following the Italian tournament and first on a hard surface from March of 2023.
Success also means the Russian has won 21 championships at twenty-one various events.
"It's the first time I'm at a tournament with my both daughters together, so to win a title is really nice," said tennis professional Medvedev.
"This victory is in dedication of my child Victoria, because the initial championship I got when my older daughter my daughter was born was for her."
The tennis star, the former major winner, had failed in his past six title deciders, comprising in the German tournament earlier this year.
His counter-punching play style and recurring emotional displays on court had prompted observers to doubt if his skill to perform at the highest level was over.
Yet the player has implemented adjustments in the last few weeks, striving to advance forward and compete aggressively, backed up by an improved serving game.
The champion fought back from a disadvantage in the opening set against the challenging Frenchman, securing 4 of the concluding five games to go ahead.
Both players traded service breaks in the second set before the Frenchman, striving for his initial ATP Tour championship, took control to push for a final set.
He defended four early chances in a close final set before the champion won the break to fifteen to close out the victory.
Appropriately, he secured victory with a rally at the net, with his opponent incapable to control a shot after a lengthy match.