Nineteen of Medvedev's twenty-one championships have been achieved on hard surfaces
A comeback Medvedev claimed his maiden trophy for over two years with a win over Frenchman Moutet in the Almaty Open final.
The Russian, a former number one, has endured a challenging year, achieving just one match at the major tournaments and suffering a setback at the New York tournament.
His inconsistency on the ATP Tour - and difficulties with his serving in particular - resulted in him dropping out of the elite rankings and eventually separating with long-term trainer Cervara.
Now collaborating with Thomas Johansson and Goetzke, the tennis star has steadily improved in the recent weeks - peaking in a hard-fought three-set triumph over Frenchman Moutet.
This represents Medvedev's initial title after the Italian tournament and maiden on a hardcourt after spring of that year.
The win also signifies he has won twenty-one championships at 21 various competitions.
"This marks the first occasion I have attended a event with my both daughters simultaneously, so to win a championship is particularly special," said world number 14 Medvedev.
"This championship is in tribute of my second daughter her name, because the maiden victory I achieved when my older daughter Alisa was born was for her."
Medvedev, the 2021 US Open champion, had lost his past six finals, including in Halle earlier this year.
The player's defensive strategy and recurring emotional displays on the playing surface had led observers to wonder if his ability to play at the highest level was concluded.
Yet the player has altered his approach in recent weeks, striving to come to the net and play positively, supported by an better serving game.
He fought back from a disadvantage in the initial set against the difficult Frenchman, winning 4 of the final five points to go ahead.
The pair traded break points in the following set before the Frenchman, striving for his initial ATP Tour championship, gained dominance to create a decider.
Moutet rescued four early chances in a competitive third set before the champion secured a break to fifteen to close out the victory.
Appropriately, Medvedev earned the win with a point at the net area, with the Frenchman unable to handle a return after a lengthy match.
