Nineteen of Medvedev's twenty-one championships have been won on hardcourt
A resurgent the Russian player claimed his initial trophy for nearly 30 months with success over Frenchman Moutet in the Almaty Open championship match.
The athlete, a former top-ranked player, has had a torrid year, winning just one match at the Grand Slams and experiencing a difficult moment at the US Open.
Medvedev's varied form on the ATP Tour - and struggles with his serve in particular - led to him falling of the elite rankings and ultimately separating with former mentor Cervara.
Currently working with Thomas Johansson and Rohan Goetzke, he has steadily progressed in the recent weeks - climaxing in a tightly fought competitive victory over opponent Corentin Moutet.
It is Medvedev's maiden trophy since the 2023 Rome Masters and first on a hard court after March of the previous year.
Victory also means the Russian has won 21 victories at twenty-one different tournaments.
"It's the first time I'm at a event with my both daughters at once, so to win a trophy is especially meaningful," said world number 14 Daniil Medvedev.
"This title is in tribute of my younger daughter her name, because the initial championship I achieved when my older daughter my daughter was born was for her."
The athlete, the past champion, had failed in his past six title deciders, featuring in that event previously this season.
Medvedev's defensive play style and regular reactions on the tennis court had caused commentators to doubt if his skill to perform at the highest level was finished.
But the athlete has implemented adjustments in recent weeks, making an effort to advance forward and play aggressively, backed up by an enhanced serve.
He came back from a disadvantage in the opening set against the tricky Moutet, securing 4 of the final five exchanges to gain the advantage.
The competitors exchanged break points in the middle set before the Frenchman, bidding for his first ATP Tour championship, gained dominance to push for a final set.
He rescued 4 initial break points in a tight final set before Medvedev secured a break to 15 to secure the win.
Appropriately, Medvedev clinched the title with a shot at the net area, with the Frenchman incapable to handle a return after two hours and 38 minutes.