19 of the Russian's 21 titles have been won on hard courts
A resurgent Medvedev secured his first championship for 882 days with success over opponent Moutet in the Almaty Open championship match.
Medvedev, a ex- number one, has experienced a challenging year, winning just a single victory at the Grand Slams and undergoing a setback at the American major.
Medvedev's inconsistency on the professional circuit - and issues with his serving in specific - caused him dropping out of the world's top 10 and ultimately parting ways with long-term trainer Cervara.
Now collaborating with his coach and his other coach, the tennis star has gradually progressed in the past month - peaking in a tightly fought 7-5 4-6 6-3 win over challenger Moutet.
It is his first title following the Rome competition and maiden on a hard surface since spring of 2023.
Victory also indicates he has secured twenty-one victories at 21 various events.
"This marks the first occasion I am participating in a event with my both daughters together, so to win a trophy is really nice," commented world number 14 Medvedev.
"This title is in dedication of my second daughter her name, because the initial championship I got when my child my daughter was born was for her."
The athlete, the past champion, had lost his previous six title deciders, including in Halle previously this season.
The player's defensive play style and regular emotional displays on court had prompted some to question if his capacity to play at the highest level was concluded.
However the athlete has altered his approach in recent weeks, striving to come to the net and play assertively, reinforced by an enhanced serve.
Medvedev came back from a deficit in the opening set against the difficult Frenchman, taking four of the final five points to take the lead.
The competitors swapped breaks in the middle set before the Frenchman, striving for his maiden ATP Tour title, gained dominance to force a final set.
He rescued four early-game break points in a competitive third set before the champion secured a break to 15 to secure the win.
Suitably, the winner clinched victory with a rally at the net, with Moutet unable to manage a shot after over two and a half hours.