19 of Medvedev's twenty-one titles have been achieved on hard surfaces
A comeback the Russian player claimed his first championship for nearly 30 months with success over opponent Moutet in the tournament title decider.
The athlete, a former top-ranked player, has endured a torrid period, winning just a single victory at the big events and undergoing a meltdown at the American major.
His unpredictability on the ATP Tour - and issues with his serve in specific - led to him exiting of the world's top 10 and eventually splitting with long-time mentor his previous coach.
Presently working with his coach and Rohan Goetzke, he has gradually progressed in the recent weeks - climaxing in a hard-fought three-set victory over Frenchman Moutet.
This marks Medvedev's maiden championship following the 2023 Rome Masters and initial on a hard court after spring of that year.
The win also means the Russian has won 21 championships at 21 different events.
"It's the first time I have attended a event with my both daughters simultaneously, so to win a championship is especially meaningful," commented world number 14 the champion.
"This championship is in tribute of my younger daughter Victoria, because the first title I won when my older daughter Alisa was born was for her."
The athlete, the 2021 US Open champion, had lost his previous six championship matches, including in that event earlier this year.
His counter-punching approach and frequent outbursts on the tennis court had led observers to question if his skill to perform at the elite level was over.
However the athlete has implemented adjustments in recent weeks, attempting to come to the net and compete assertively, supported by an improved serve.
He fought back from a deficit in the first set against the difficult Moutet, winning four of the concluding five exchanges to go ahead.
Both players swapped breaks in the second set before Moutet, striving for his initial tour title, took control to force a third set.
The opponent defended 4 early opportunities in a competitive final set before the Russian secured a break to fifteen to secure the win.
Fittingly, he clinched victory with a point at the net, with his opponent failing to handle a shot after a lengthy match.