Nineteen of Medvedev's twenty-one titles have been achieved on hard surfaces
A revitalized the Russian player secured his initial trophy for 882 days with a win over opponent Moutet in the Almaty Open title decider.
The athlete, a former world number one, has experienced a difficult period, achieving just one win at the big events and undergoing a setback at the American major.
Medvedev's unpredictability on the ATP Tour - and struggles with his service game in particular - resulted in him dropping out of the top ten and finally splitting with long-term coach Gilles Cervara.
Now collaborating with his coach and Rohan Goetzke, he has consistently progressed in the recent weeks - climaxing in a closely contested three-set victory over Frenchman Moutet.
This marks Medvedev's initial trophy after the Rome competition and initial on a hard court from that period of 2023.
Success also indicates Medvedev has secured twenty-one championships at twenty-one various tournaments.
"For the first time I am participating in a tournament with my two daughters at once, so to secure a title is particularly special," commented ranked player the champion.
"This title is in honour of my second daughter her name, because the first title I achieved when my older daughter my daughter was delivered was for her."
The tennis star, the 2021 US Open champion, had failed in his last six championship matches, including in the German tournament previously this season.
The player's defensive approach and regular emotional displays on the tennis court had prompted some to question if his skill to play at the top level was finished.
However the 29-year-old has implemented adjustments in recent weeks, making an effort to advance forward and perform assertively, reinforced by an enhanced service.
The champion fought back from a break down in the first set against the difficult Moutet, securing 4 of the concluding five points to gain the advantage.
The pair traded service breaks in the middle set before the challenger, bidding for his maiden ATP Tour title, gained dominance to create a final set.
The opponent rescued 4 initial chances in a tight third set before Medvedev won the break to 15 to serve for the match.
Fittingly, Medvedev secured the title with a shot at the net area, with Moutet failing to control a return after over two and a half hours.