19 of Medvedev's twenty-one titles have been earned on hard courts
A comeback the Russian player secured his first trophy for 882 days with victory over Frenchman Moutet in the Almaty Open final.
The Russian, a ex- world number one, has had a challenging period, winning just one match at the major tournaments and undergoing a difficult moment at the New York tournament.
The player's varied form on the tennis tour - and difficulties with his service game in especial - resulted in him dropping out of the elite rankings and finally splitting with long-time coach his previous coach.
Now collaborating with Thomas Johansson and Rohan Goetzke, he has steadily improved in the past month - peaking in a hard-fought 7-5 4-6 6-3 win over Frenchman Moutet.
It is Medvedev's first championship following the Rome competition and maiden on a hard surface from spring of that year.
Victory also means the Russian has won 21 championships at 21 various tournaments.
"For the first time I am participating in a event with my both daughters together, so to secure a title is particularly special," stated world number 14 Medvedev.
"This title is in honour of my second daughter her name, because the first title I achieved when my first daughter her name was delivered was for her."
Medvedev, the former major winner, had failed in his last six championship matches, including in Halle previously this season.
His retrieving strategy and frequent outbursts on court had caused observers to doubt if his ability to compete at the highest level was finished.
But the athlete has implemented adjustments in the last few weeks, making an effort to advance forward and play positively, backed up by an enhanced serve.
Medvedev recovered from a break down in the opening set against the tricky Moutet, securing 4 of the concluding five exchanges to take the lead.
The competitors exchanged service breaks in the following set before the Frenchman, bidding for his maiden ATP Tour title, gained dominance to create a decider.
He saved four early opportunities in a tight deciding set before Medvedev broke to that score to serve for the match.
Fittingly, the winner earned victory with a shot at the net, with his opponent unable to handle a shot after two hours and 38 minutes.
