19 of Medvedev's 21 titles have been earned on hard courts
A comeback the Russian player won his initial championship for 882 days with success over opponent Moutet in the Almaty Open title decider.
Medvedev, a ex- number one, has endured a torrid season, managing just one win at the major tournaments and experiencing a meltdown at the New York tournament.
His inconsistency on the ATP Tour - and issues with his service game in especial - caused him exiting of the top ten and finally splitting with former mentor Gilles Cervara.
Now working with his coach and Rohan Goetzke, Medvedev has gradually advanced in the past month - climaxing in a hard-fought three-set triumph over challenger Moutet.
It is the player's initial championship following the Italian tournament and initial on a hardcourt since spring of 2023.
Victory also signifies he has secured twenty-one championships at 21 distinct events.
"It's the first time I'm at a tournament with my both daughters simultaneously, so to win a trophy is particularly special," commented ranked player the champion.
"This championship is in dedication of my second daughter her name, because the maiden victory I got when my older daughter my daughter was born was for her."
The athlete, the 2021 US Open champion, had lost his past six title deciders, featuring in Halle previously this season.
Medvedev's counter-punching approach and frequent emotional displays on the tennis court had prompted some to wonder if his capacity to play at the highest level was over.
However the 29-year-old has made changes in the last few weeks, striving to approach the net and compete aggressively, backed up by an better serving game.
He recovered from a break down in the first set against the challenging Moutet, securing 4 of the final five games to gain the advantage.
The pair exchanged breaks in the middle set before Moutet, striving for his maiden tour title, seized the initiative to push for a final set.
The opponent rescued 4 early opportunities in a tight final set before Medvedev broke to fifteen to serve for the match.
Appropriately, Medvedev secured victory with a point at the net area, with his opponent unable to handle a volley after a lengthy match.