Nineteen of Medvedev's 21 victories have been earned on hard surfaces
A comeback the Russian player claimed his initial title for 882 days with victory over Frenchman Moutet in the Almaty Open final.
Medvedev, a former top-ranked player, has experienced a challenging year, achieving just one win at the big events and experiencing a meltdown at the US Open.
The player's varied form on the tennis tour - and issues with his serving in especial - resulted in him exiting of the top ten and eventually splitting with long-term mentor Gilles Cervara.
Currently training with his coach and Rohan Goetzke, the tennis star has steadily improved in the past month - culminating in a tightly fought three-set win over Frenchman Moutet.
This marks his first title after the Italian tournament and maiden on a hard court after March of 2023.
Victory also signifies he has achieved 21 championships at 21 distinct tournaments.
"It's the first time I have attended a tournament with my both daughters at once, so to secure a title is especially meaningful," said ranked player the champion.
"This championship is in tribute of my child Victoria, because the initial championship I achieved when my older daughter Alisa was born was for her."
The athlete, the 2021 US Open champion, had lost his previous six finals, including in the German tournament previously this season.
Medvedev's counter-punching strategy and recurring reactions on the tennis court had led some to wonder if his capacity to perform at the top level was concluded.
Yet the player has implemented adjustments in the last few weeks, attempting to come to the net and compete positively, reinforced by an enhanced service.
He came back from a disadvantage in the opening set against the challenging opponent, winning 4 of the last five games to take the lead.
Both players traded breaks in the following set before the Frenchman, bidding for his first professional victory, took control to create a final set.
He defended four initial chances in a competitive deciding set before the Russian won the break to fifteen to close out the victory.
Suitably, Medvedev earned victory with a rally at the net area, with the Frenchman failing to control a return after two hours and 38 minutes.
