Nineteen of Medvedev's twenty-one victories have been achieved on hard courts
A revitalized the Russian player claimed his maiden championship for 882 days with a win over opponent Moutet in the Almaty Open final.
The Russian, a former number one, has endured a torrid period, achieving just one match at the major tournaments and suffering a setback at the American major.
Medvedev's varied form on the ATP Tour - and difficulties with his service game in especial - led to him falling of the elite rankings and finally separating with long-term coach Gilles Cervara.
Currently training with his coach and Rohan Goetzke, he has gradually progressed in the past month - climaxing in a tightly fought 7-5 4-6 6-3 victory over opponent Moutet.
It is the player's maiden title since the 2023 Rome Masters and first on a hard surface from that period of 2023.
The win also means Medvedev has achieved 21 titles at twenty-one different competitions.
"This marks the first occasion I'm at a tournament with my children at once, so to get a title is particularly special," said tennis professional the champion.
"This title is in tribute of my second daughter her name, because the maiden victory I achieved when my child Alisa was born was for her."
The athlete, the past champion, had been defeated in his past six championship matches, including in that event in the past months.
The player's defensive play style and recurring reactions on the tennis court had caused commentators to wonder if his skill to perform at the elite level was concluded.
But the 29-year-old has implemented adjustments in recent weeks, attempting to advance forward and play positively, backed up by an enhanced service.
Medvedev came back from a break down in the first set against the challenging opponent, securing four of the last five exchanges to go ahead.
The pair swapped service breaks in the second set before Moutet, attempting for his first tour victory, took control to push for a final set.
Moutet rescued 4 early-game break points in a tight third set before the Russian won the break to that score to secure the win.
Suitably, the winner earned the win with a point at the net area, with Moutet failing to handle a shot after a lengthy match.