Nineteen of the Russian's twenty-one championships have been won on hardcourt
A comeback Medvedev secured his maiden championship for nearly 30 months with victory over Frenchman Moutet in the Almaty Open title decider.
The Russian, a former world number one, has had a torrid period, managing just a single victory at the big events and suffering a setback at the New York tournament.
Medvedev's unpredictability on the tennis tour - and issues with his serve in particular - led to him falling of the top ten and ultimately splitting with long-time trainer his previous coach.
Presently working with Johansson and Goetzke, the tennis star has steadily improved in the last few weeks - peaking in a closely contested three-set win over Frenchman Corentin Moutet.
This represents his initial championship since the 2023 Rome Masters and initial on a hardcourt since spring of that year.
Success also means the Russian has secured 21 championships at 21 different tournaments.
"This marks the first occasion I'm at a competition with my both daughters together, so to secure a title is especially meaningful," said world number 14 Medvedev.
"This championship is in honour of my younger daughter my daughter, because the initial championship I won when my first daughter Alisa was born was for her."
Medvedev, the former major winner, had been defeated in his previous six championship matches, including in that event in the past months.
His counter-punching play style and regular reactions on the tennis court had prompted some to question if his ability to play at the top level was finished.
But the athlete has made changes in the past month, striving to come to the net and play aggressively, reinforced by an improved service.
He came back from a break down in the opening set against the tricky opponent, securing four of the final five exchanges to go ahead.
The competitors traded break points in the following set before Moutet, bidding for his maiden professional championship, seized the initiative to push for a third set.
He defended 4 early-game break points in a close third set before Medvedev won the break to fifteen to secure the win.
Appropriately, Medvedev clinched the title with a point at the front of the court, with his opponent incapable to handle a volley after two hours and 38 minutes.
