Nineteen of Medvedev's twenty-one titles have been achieved on hard surfaces
A resurgent the Russian player won his first championship for 882 days with a win over Frenchman Moutet in the Almaty Open championship match.
Medvedev, a ex- world number one, has had a difficult period, winning just one win at the Grand Slams and suffering a difficult moment at the American major.
His inconsistency on the professional circuit - and issues with his serving in particular - led to him falling of the top ten and ultimately separating with long-time mentor his previous coach.
Presently collaborating with Thomas Johansson and Rohan Goetzke, the tennis star has steadily progressed in the past month - culminating in a hard-fought three-set triumph over challenger Moutet.
This marks his initial trophy since the Italian tournament and initial on a hard court after March of 2023.
The win also signifies Medvedev has secured twenty-one titles at 21 different competitions.
"For the first time I am participating in a event with my two daughters at once, so to get a title is particularly special," said tennis professional Daniil Medvedev.
"This victory is in dedication of my second daughter Victoria, because the maiden victory I got when my child my daughter was born was for her."
The athlete, the former major winner, had been defeated in his previous six finals, comprising in Halle in the past months.
Medvedev's retrieving play style and frequent outbursts on the tennis court had caused some to question if his skill to play at the highest level was concluded.
However the 29-year-old has made changes in the last few weeks, attempting to advance forward and play aggressively, supported by an enhanced serving game.
Medvedev came back from a deficit in the first set against the difficult Moutet, securing four of the concluding five games to go ahead.
The competitors exchanged break points in the middle set before the Frenchman, bidding for his initial tour title, took control to force a final set.
The opponent saved four early-game chances in a tight third set before the Russian broke to that score to close out the victory.
Appropriately, he secured the title with a point at the net area, with his opponent incapable to handle a return after over two and a half hours.