Nineteen of the Russian's twenty-one titles have been earned on hard surfaces
A resurgent the Russian player secured his first trophy for over two years with victory over Frenchman Moutet in the Almaty Open championship match.
Medvedev, a former top-ranked player, has had a challenging season, managing just a single victory at the Grand Slams and experiencing a difficult moment at the US Open.
His varied form on the tennis tour - and difficulties with his serve in especial - led to him exiting of the world's top 10 and eventually splitting with long-time trainer Gilles Cervara.
Currently training with his coach and his other coach, Medvedev has steadily progressed in the past month - culminating in a hard-fought three-set victory over Frenchman Moutet.
This represents his initial trophy since the 2023 Rome Masters and first on a hard court since March of 2023.
Success also indicates the Russian has achieved 21 victories at 21 different tournaments.
"This marks the first occasion I am participating in a event with my two daughters simultaneously, so to win a championship is really nice," commented ranked player Medvedev.
"This title is in dedication of my younger daughter Victoria, because the maiden victory I achieved when my child my daughter was born was for her."
Medvedev, the past champion, had lost his last six championship matches, comprising in that event previously this season.
The player's counter-punching approach and recurring reactions on court had caused observers to doubt if his skill to play at the highest level was finished.
Yet the athlete has implemented adjustments in recent weeks, attempting to approach the net and perform positively, reinforced by an enhanced service.
The champion came back from a deficit in the initial set against the challenging Frenchman, taking 4 of the final five exchanges to go ahead.
Both players traded breaks in the following set before the Frenchman, bidding for his first tour championship, took control to create a decider.
The opponent saved four early-game opportunities in a tight deciding set before the Russian secured a break to 15 to serve for the match.
Appropriately, he clinched the title with a shot at the net area, with Moutet unable to handle a return after two hours and 38 minutes.