19 of Medvedev's 21 victories have been won on hard courts
A comeback Medvedev claimed his maiden title for 882 days with a win over opponent Moutet in the Almaty Open title decider.
The Russian, a former top-ranked player, has had a torrid year, winning just one match at the major tournaments and undergoing a difficult moment at the New York tournament.
His varied form on the tennis tour - and struggles with his serve in particular - resulted in him dropping out of the world's top 10 and finally parting ways with long-term coach Cervara.
Presently training with Thomas Johansson and Rohan Goetzke, Medvedev has consistently improved in the past month - peaking in a tightly fought 7-5 4-6 6-3 victory over opponent Moutet.
This marks the player's initial trophy after the Italian tournament and first on a hardcourt after that period of the previous year.
The win also signifies he has won twenty-one victories at twenty-one different competitions.
"This marks the first occasion I'm at a tournament with my both daughters together, so to get a championship is really nice," said ranked player Daniil Medvedev.
"This victory is in dedication of my younger daughter Victoria, because the first title I won when my first daughter my daughter was delivered was for her."
The tennis star, the 2021 US Open champion, had failed in his past six title deciders, including in Halle previously this season.
Medvedev's retrieving play style and recurring outbursts on the tennis court had prompted observers to doubt if his capacity to compete at the highest level was concluded.
However the 29-year-old has made changes in recent weeks, striving to come to the net and perform assertively, supported by an enhanced serve.
Medvedev fought back from a deficit in the first set against the challenging opponent, securing 4 of the last five points to take the lead.
The pair exchanged break points in the second set before the challenger, bidding for his initial ATP Tour victory, gained dominance to push for a decider.
Moutet defended four early-game chances in a competitive deciding set before Medvedev broke to 15 to secure the win.
Appropriately, he secured the win with a point at the net, with Moutet incapable to handle a shot after over two and a half hours.