19 of Medvedev's 21 titles have been won on hard courts
A resurgent the Russian player claimed his maiden trophy for nearly 30 months with success over opponent Moutet in the Almaty Open final.
Medvedev, a ex- top-ranked player, has experienced a challenging year, achieving just one match at the big events and experiencing a difficult moment at the US Open.
Medvedev's varied form on the professional circuit - and issues with his serving in particular - led to him exiting of the elite rankings and ultimately splitting with long-term trainer his previous coach.
Presently training with Johansson and his other coach, the tennis star has gradually progressed in the last few weeks - peaking in a hard-fought three-set win over Frenchman Moutet.
It is the player's initial trophy following the Italian tournament and first on a hardcourt from spring of 2023.
Victory also signifies the Russian has won 21 championships at 21 different competitions.
"This marks the first occasion I'm at a event with my both daughters at once, so to win a title is especially meaningful," commented world number 14 Medvedev.
"This victory is in tribute of my younger daughter her name, because the maiden victory I got when my child her name was born was for her."
Medvedev, the 2021 US Open champion, had failed in his previous six finals, comprising in Halle previously this season.
The player's defensive strategy and regular outbursts on court had prompted commentators to doubt if his skill to perform at the top level was over.
However the player has implemented adjustments in the past month, attempting to advance forward and play assertively, backed up by an improved serving game.
Medvedev came back from a deficit in the opening set against the challenging Moutet, securing 4 of the concluding five games to gain the advantage.
Both players swapped break points in the middle set before the Frenchman, attempting for his first ATP Tour title, seized the initiative to force a third set.
He defended four early break points in a competitive final set before the Russian secured a break to fifteen to close out the victory.
Appropriately, the winner clinched the title with a shot at the net area, with his opponent unable to handle a shot after a lengthy match.