19 of the Russian's twenty-one victories have been achieved on hard courts
A resurgent the Russian player secured his maiden championship for nearly 30 months with success over Frenchman Moutet in the Almaty Open title decider.
Medvedev, a ex- top-ranked player, has experienced a difficult year, winning just one match at the Grand Slams and experiencing a meltdown at the New York tournament.
The player's inconsistency on the professional circuit - and struggles with his service game in especial - caused him falling of the world's top 10 and eventually splitting with long-time coach Gilles Cervara.
Presently working with Johansson and Rohan Goetzke, Medvedev has consistently progressed in the past month - peaking in a closely contested competitive win over opponent Moutet.
It is the player's initial trophy after the 2023 Rome Masters and first on a hard surface from spring of 2023.
Victory also means the Russian has achieved 21 championships at twenty-one different competitions.
"This marks the first occasion I am participating in a competition with my children simultaneously, so to secure a championship is especially meaningful," said world number 14 Medvedev.
"This title is in tribute of my child her name, because the first title I achieved when my child her name was born was for her."
Medvedev, the past champion, had failed in his last six championship matches, featuring in that event earlier this year.
His retrieving strategy and regular emotional displays on court had prompted observers to wonder if his skill to perform at the top level was concluded.
Yet the athlete has made changes in recent weeks, making an effort to come to the net and perform aggressively, supported by an better serving game.
The champion came back from a deficit in the initial set against the difficult Moutet, securing four of the last five points to take the lead.
Both players traded break points in the middle set before Moutet, striving for his initial ATP Tour championship, seized the initiative to force a third set.
The opponent rescued four early-game break points in a close third set before the champion won the break to that score to serve for the match.
Fittingly, the winner earned victory with a point at the net, with his opponent unable to control a shot after a lengthy match.