19 of the Russian's 21 victories have been earned on hardcourt
A comeback Medvedev claimed his first trophy for over two years with a win over opponent Moutet in the Almaty Open championship match.
The Russian, a ex- number one, has had a torrid season, managing just one match at the big events and undergoing a meltdown at the US Open.
Medvedev's varied form on the ATP Tour - and struggles with his serve in specific - caused him exiting of the elite rankings and ultimately splitting with long-term mentor his previous coach.
Currently collaborating with Thomas Johansson and his other coach, he has consistently progressed in the last few weeks - culminating in a closely contested three-set victory over challenger Corentin Moutet.
It is the player's maiden championship following the Italian tournament and initial on a hard court since March of the previous year.
The win also means the Russian has won 21 championships at twenty-one various events.
"For the first time I'm at a event with my two daughters simultaneously, so to get a trophy is especially meaningful," said world number 14 Medvedev.
"This championship is in dedication of my younger daughter her name, because the initial championship I achieved when my child her name was delivered was for her."
The tennis star, the former major winner, had been defeated in his past six championship matches, including in that event in the past months.
Medvedev's defensive strategy and frequent outbursts on the tennis court had caused observers to question if his capacity to play at the top level was over.
But the 29-year-old has implemented adjustments in the last few weeks, striving to come to the net and compete aggressively, backed up by an enhanced service.
The champion came back from a break down in the opening set against the tricky Moutet, taking four of the final five games to gain the advantage.
The competitors exchanged service breaks in the middle set before Moutet, attempting for his first professional title, seized the initiative to create a third set.
Moutet defended four early-game break points in a tight deciding set before the Russian secured a break to 15 to serve for the match.
Appropriately, the winner clinched the title with a shot at the net area, with his opponent unable to handle a return after over two and a half hours.
