19 of Medvedev's 21 championships have been achieved on hard courts
A revitalized the Russian player secured his maiden title for 882 days with a win over Frenchman Moutet in the Almaty Open championship match.
Medvedev, a ex- world number one, has endured a difficult year, managing just one win at the Grand Slams and experiencing a setback at the New York tournament.
His unpredictability on the professional circuit - and struggles with his service game in specific - caused him falling of the top ten and ultimately separating with long-term trainer Gilles Cervara.
Now collaborating with his coach and his other coach, Medvedev has steadily improved in the last few weeks - climaxing in a tightly fought three-set win over opponent Moutet.
This marks his first championship since the Rome competition and maiden on a hard surface from that period of that year.
Victory also means Medvedev has won 21 championships at twenty-one different tournaments.
"This marks the first occasion I have attended a tournament with my two daughters simultaneously, so to secure a title is particularly special," said world number 14 Daniil Medvedev.
"This title is in dedication of my child my daughter, because the maiden victory I got when my child my daughter was born was for her."
The tennis star, the past champion, had failed in his previous six finals, including in Halle previously this season.
The player's retrieving strategy and frequent emotional displays on court had caused commentators to doubt if his capacity to compete at the elite level was concluded.
However the athlete has made changes in the last few weeks, making an effort to advance forward and perform positively, reinforced by an improved serve.
He recovered from a disadvantage in the initial set against the challenging Frenchman, securing four of the concluding five games to gain the advantage.
The competitors swapped breaks in the middle set before the challenger, bidding for his maiden tour championship, gained dominance to create a final set.
He defended 4 early-game opportunities in a close third set before the champion won the break to 15 to close out the victory.
Appropriately, Medvedev earned the win with a point at the net area, with the Frenchman failing to control a return after two hours and 38 minutes.