Nineteen of the Russian's twenty-one championships have been achieved on hard courts
A revitalized Medvedev secured his maiden championship for nearly 30 months with victory over Frenchman Moutet in the Almaty Open championship match.
The Russian, a ex- world number one, has had a challenging period, managing just a single victory at the Grand Slams and undergoing a difficult moment at the New York tournament.
The player's inconsistency on the tennis tour - and struggles with his serving in specific - led to him exiting of the elite rankings and eventually separating with former trainer his previous coach.
Presently working with his coach and Goetzke, Medvedev has consistently advanced in the past month - culminating in a closely contested 7-5 4-6 6-3 win over Frenchman Moutet.
This marks his first title after the Rome competition and maiden on a hard court after spring of that year.
The win also signifies the Russian has achieved twenty-one titles at 21 different tournaments.
"This marks the first occasion I'm at a tournament with my children at once, so to win a championship is really nice," commented ranked player the champion.
"This victory is in tribute of my child her name, because the initial championship I achieved when my older daughter Alisa was born was for her."
Medvedev, the former major winner, had lost his previous six championship matches, comprising in Halle in the past months.
The player's retrieving play style and regular reactions on court had caused some to question if his ability to perform at the top level was over.
But the player has made changes in recent weeks, making an effort to approach the net and perform positively, backed up by an enhanced service.
Medvedev came back from a break down in the opening set against the tricky opponent, securing four of the last five exchanges to take the lead.
The competitors exchanged breaks in the middle set before the challenger, attempting for his initial tour victory, seized the initiative to force a third set.
Moutet defended 4 initial opportunities in a close third set before the champion secured a break to fifteen to close out the victory.
Suitably, Medvedev clinched the title with a shot at the front of the court, with the Frenchman incapable to control a shot after a lengthy match.