19 of Medvedev's twenty-one championships have been earned on hard surfaces
A comeback the Russian player claimed his maiden trophy for over two years with victory over opponent Moutet in the Almaty Open championship match.
Medvedev, a ex- number one, has experienced a torrid period, achieving just one match at the Grand Slams and suffering a setback at the US Open.
His inconsistency on the professional circuit - and issues with his serve in particular - led to him exiting of the elite rankings and eventually separating with long-term trainer his previous coach.
Now collaborating with his coach and Rohan Goetzke, he has steadily progressed in the last few weeks - climaxing in a tightly fought 7-5 4-6 6-3 win over Frenchman Moutet.
This marks his maiden title after the Italian tournament and initial on a hard court since spring of the previous year.
The win also indicates the Russian has achieved twenty-one titles at twenty-one distinct events.
"This marks the first occasion I'm at a tournament with my both daughters together, so to secure a championship is especially meaningful," commented world number 14 Daniil Medvedev.
"This title is in tribute of my second daughter Victoria, because the initial championship I got when my older daughter Alisa was born was for her."
The athlete, the 2021 US Open champion, had lost his previous six finals, comprising in that event previously this season.
The player's counter-punching play style and frequent emotional displays on the tennis court had led observers to wonder if his skill to play at the highest level was over.
Yet the player has altered his approach in the last few weeks, striving to come to the net and compete aggressively, supported by an enhanced serve.
Medvedev recovered from a break down in the initial set against the challenging Moutet, winning four of the final five games to take the lead.
The competitors traded service breaks in the second set before Moutet, striving for his initial tour championship, gained dominance to force a third set.
Moutet saved four initial chances in a tight third set before the Russian broke to that score to close out the victory.
Fittingly, he clinched the title with a point at the net, with Moutet failing to manage a return after over two and a half hours.