Nineteen of the Russian's 21 titles have been won on hard courts
A comeback the Russian player secured his initial trophy for over two years with a win over Frenchman Moutet in the Almaty Open title decider.
The athlete, a former number one, has had a torrid period, winning just one match at the big events and experiencing a meltdown at the New York tournament.
The player's inconsistency on the tennis tour - and issues with his serving in specific - led to him dropping out of the top ten and eventually splitting with former trainer his previous coach.
Currently training with Johansson and Rohan Goetzke, Medvedev has steadily improved in the past month - peaking in a hard-fought 7-5 4-6 6-3 victory over opponent Corentin Moutet.
This marks his initial trophy after the Rome competition and first on a hard court from spring of 2023.
Success also signifies he has secured 21 titles at 21 distinct events.
"For the first time I have attended a event with my both daughters at once, so to win a trophy is really nice," said world number 14 Medvedev.
"This victory is in dedication of my child my daughter, because the maiden victory I got when my child my daughter was delivered was for her."
The tennis star, the 2021 US Open champion, had failed in his past six championship matches, including in that event previously this season.
The player's retrieving play style and regular emotional displays on the playing surface had caused observers to wonder if his skill to play at the top level was finished.
Yet the athlete has implemented adjustments in the last few weeks, making an effort to come to the net and perform aggressively, reinforced by an better serving game.
The champion fought back from a deficit in the initial set against the tricky Moutet, winning 4 of the last five exchanges to go ahead.
The pair traded service breaks in the second set before Moutet, striving for his first tour title, gained dominance to push for a third set.
Moutet defended four initial break points in a competitive third set before Medvedev secured a break to 15 to serve for the match.
Suitably, Medvedev clinched victory with a rally at the net area, with Moutet failing to control a return after over two and a half hours.
