19 of Medvedev's twenty-one championships have been earned on hardcourt
A comeback the Russian player secured his first trophy for 882 days with victory over Frenchman Moutet in the Almaty Open championship match.
The athlete, a ex- world number one, has endured a difficult period, achieving just a single victory at the Grand Slams and undergoing a meltdown at the New York tournament.
His varied form on the tennis tour - and difficulties with his service game in particular - led to him dropping out of the elite rankings and eventually separating with long-term coach Cervara.
Now training with his coach and Goetzke, the tennis star has gradually progressed in the last few weeks - climaxing in a tightly fought three-set victory over Frenchman Moutet.
It is Medvedev's initial trophy following the 2023 Rome Masters and initial on a hardcourt since spring of the previous year.
Victory also signifies Medvedev has won 21 victories at 21 distinct events.
"It's the first time I have attended a competition with my children together, so to secure a trophy is especially meaningful," stated tennis professional Medvedev.
"This victory is in dedication of my younger daughter her name, because the initial championship I won when my older daughter Alisa was delivered was for her."
Medvedev, the former major winner, had been defeated in his last six championship matches, featuring in Halle previously this season.
Medvedev's defensive play style and frequent outbursts on the playing surface had caused some to wonder if his capacity to play at the highest level was finished.
But the 29-year-old has made changes in recent weeks, making an effort to advance forward and play assertively, backed up by an improved serve.
The champion fought back from a break down in the first set against the challenging Moutet, winning four of the concluding five games to take the lead.
The pair exchanged break points in the following set before the Frenchman, striving for his initial professional title, seized the initiative to push for a third set.
He defended four early break points in a competitive final set before the Russian won the break to fifteen to close out the victory.
Appropriately, the winner earned the win with a shot at the front of the court, with Moutet failing to control a volley after a lengthy match.