Nineteen of Medvedev's twenty-one championships have been achieved on hard courts
A resurgent the Russian player claimed his maiden title for 882 days with a win over Frenchman Moutet in the Almaty Open championship match.
The athlete, a former top-ranked player, has experienced a torrid season, winning just a single victory at the big events and suffering a meltdown at the US Open.
Medvedev's unpredictability on the ATP Tour - and difficulties with his serving in specific - led to him exiting of the elite rankings and eventually splitting with former trainer Cervara.
Presently working with Thomas Johansson and Rohan Goetzke, he has consistently improved in the last few weeks - climaxing in a hard-fought competitive victory over Frenchman Corentin Moutet.
This marks his initial championship after the Italian tournament and initial on a hardcourt from March of that year.
Success also means he has secured 21 championships at 21 distinct tournaments.
"For the first time I have attended a competition with my two daughters at once, so to get a title is really nice," said tennis professional Daniil Medvedev.
"This victory is in dedication of my child Victoria, because the first title I achieved when my older daughter my daughter was delivered was for her."
Medvedev, the past champion, had failed in his past six title deciders, comprising in that event previously this season.
The player's defensive approach and regular reactions on court had led some to doubt if his skill to play at the top level was finished.
However the 29-year-old has implemented adjustments in the past month, making an effort to advance forward and perform assertively, backed up by an improved service.
Medvedev fought back from a break down in the opening set against the tricky Frenchman, taking 4 of the last five games to go ahead.
Both players swapped break points in the second set before the Frenchman, attempting for his first tour victory, took control to create a third set.
He defended 4 initial opportunities in a competitive third set before the Russian broke to 15 to serve for the match.
Suitably, Medvedev earned victory with a rally at the net area, with the Frenchman failing to handle a return after two hours and 38 minutes.