19 of the Russian's 21 victories have been won on hard courts
A comeback Medvedev won his first championship for over two years with victory over opponent Moutet in the Almaty Open championship match.
The Russian, a ex- number one, has endured a challenging period, winning just one match at the big events and experiencing a meltdown at the US Open.
The player's inconsistency on the tennis tour - and issues with his serve in particular - resulted in him dropping out of the elite rankings and ultimately parting ways with long-time trainer his previous coach.
Presently collaborating with his coach and his other coach, he has gradually improved in the past month - peaking in a hard-fought competitive triumph over challenger Moutet.
This represents the player's initial championship since the Rome competition and initial on a hard court after spring of 2023.
The win also means Medvedev has secured 21 titles at 21 different events.
"It's the first time I have attended a event with my children simultaneously, so to get a trophy is particularly special," said ranked player the champion.
"This victory is in tribute of my younger daughter her name, because the maiden victory I got when my child my daughter was born was for her."
The tennis star, the 2021 US Open champion, had failed in his last six championship matches, featuring in Halle previously this season.
Medvedev's counter-punching approach and frequent outbursts on court had caused observers to wonder if his ability to compete at the top level was over.
But the 29-year-old has implemented adjustments in the past month, making an effort to come to the net and play aggressively, supported by an improved serve.
He fought back from a break down in the first set against the difficult Moutet, securing 4 of the last five exchanges to go ahead.
The pair swapped service breaks in the middle set before the challenger, attempting for his initial ATP Tour victory, seized the initiative to force a decider.
Moutet saved four early opportunities in a close final set before the Russian won the break to that score to serve for the match.
Fittingly, the winner secured victory with a rally at the net, with Moutet unable to control a shot after a lengthy match.
