Nineteen of the Russian's twenty-one championships have been won on hard courts
A resurgent Medvedev secured his first trophy for 882 days with victory over Frenchman Moutet in the Almaty Open final.
Medvedev, a former world number one, has endured a challenging year, managing just one win at the big events and undergoing a difficult moment at the American major.
His varied form on the tennis tour - and struggles with his serve in particular - caused him falling of the world's top 10 and finally separating with long-time coach Cervara.
Now collaborating with Thomas Johansson and Rohan Goetzke, Medvedev has consistently advanced in the past month - peaking in a hard-fought competitive triumph over Frenchman Moutet.
It is Medvedev's first title following the 2023 Rome Masters and initial on a hard court since that period of that year.
Success also indicates he has secured twenty-one championships at twenty-one different competitions.
"For the first time I'm at a competition with my children together, so to get a trophy is really nice," said tennis professional Medvedev.
"This championship is in tribute of my younger daughter Victoria, because the initial championship I won when my older daughter my daughter was born was for her."
The tennis star, the past champion, had failed in his past six championship matches, comprising in the German tournament in the past months.
The player's counter-punching play style and recurring reactions on court had caused commentators to doubt if his ability to perform at the top level was finished.
However the player has made changes in the last few weeks, making an effort to approach the net and compete assertively, reinforced by an enhanced serve.
Medvedev recovered from a disadvantage in the first set against the tricky opponent, winning four of the concluding five games to gain the advantage.
Both players exchanged service breaks in the following set before the Frenchman, bidding for his first tour championship, seized the initiative to create a decider.
The opponent saved 4 initial break points in a competitive final set before the Russian secured a break to that score to close out the victory.
Suitably, Medvedev secured the title with a rally at the front of the court, with Moutet failing to control a shot after over two and a half hours.
