Nineteen of the Russian's 21 victories have been earned on hard surfaces
A comeback Medvedev won his maiden trophy for 882 days with victory over Frenchman Moutet in the Almaty Open final.
Medvedev, a ex- top-ranked player, has had a difficult season, achieving just one match at the major tournaments and experiencing a difficult moment at the US Open.
The player's unpredictability on the ATP Tour - and issues with his serve in particular - resulted in him exiting of the top ten and finally parting ways with long-term coach Gilles Cervara.
Presently collaborating with Thomas Johansson and Goetzke, he has consistently advanced in the past month - climaxing in a closely contested 7-5 4-6 6-3 triumph over Frenchman Moutet.
This marks Medvedev's first trophy following the 2023 Rome Masters and initial on a hard surface since spring of that year.
Success also means Medvedev has won twenty-one victories at twenty-one various events.
"It's the first time I'm at a tournament with my two daughters together, so to get a championship is especially meaningful," commented world number 14 Medvedev.
"This victory is in dedication of my second daughter her name, because the first title I won when my older daughter her name was born was for her."
The tennis star, the former major winner, had lost his last six title deciders, comprising in Halle previously this season.
The player's counter-punching strategy and regular outbursts on court had led some to question if his skill to play at the elite level was finished.
But the 29-year-old has made changes in the past month, striving to come to the net and play aggressively, reinforced by an better serving game.
The champion came back from a disadvantage in the opening set against the tricky Moutet, winning four of the concluding five points to go ahead.
Both players exchanged break points in the second set before Moutet, bidding for his initial professional title, seized the initiative to push for a third set.
He saved four initial break points in a competitive deciding set before Medvedev secured a break to 15 to serve for the match.
Appropriately, the winner clinched the win with a point at the front of the court, with the Frenchman incapable to handle a return after over two and a half hours.
