Nineteen of Medvedev's 21 victories have been achieved on hard surfaces
A comeback the Russian player won his maiden trophy for nearly 30 months with victory over Frenchman Moutet in the Almaty Open final.
The athlete, a ex- top-ranked player, has had a torrid season, managing just a single victory at the big events and experiencing a difficult moment at the US Open.
Medvedev's inconsistency on the tennis tour - and struggles with his service game in specific - led to him falling of the elite rankings and eventually separating with long-time coach Gilles Cervara.
Currently training with his coach and Rohan Goetzke, the tennis star has gradually improved in the recent weeks - culminating in a closely contested three-set win over opponent Moutet.
It is Medvedev's initial championship following the 2023 Rome Masters and initial on a hard court since that period of 2023.
Success also signifies the Russian has achieved 21 championships at 21 different tournaments.
"It's the first time I have attended a event with my both daughters at once, so to secure a title is particularly special," commented ranked player Medvedev.
"This victory is in dedication of my child her name, because the initial championship I achieved when my first daughter my daughter was delivered was for her."
The tennis star, the 2021 US Open champion, had lost his last six finals, featuring in Halle previously this season.
The player's defensive play style and frequent emotional displays on the tennis court had led observers to wonder if his skill to play at the top level was finished.
However the player has altered his approach in recent weeks, attempting to approach the net and compete positively, reinforced by an better service.
He came back from a deficit in the first set against the tricky opponent, taking four of the final five points to gain the advantage.
The competitors exchanged service breaks in the second set before the Frenchman, attempting for his initial professional victory, seized the initiative to force a final set.
Moutet saved four initial opportunities in a competitive deciding set before the Russian secured a break to 15 to secure the win.
Fittingly, he clinched the win with a point at the front of the court, with Moutet failing to manage a return after two hours and 38 minutes.
