Nineteen of Medvedev's 21 titles have been won on hard courts
A comeback the Russian player won his maiden title for over two years with a win over opponent Moutet in the Almaty Open championship match.
The Russian, a ex- top-ranked player, has experienced a torrid year, winning just one match at the Grand Slams and undergoing a meltdown at the New York tournament.
Medvedev's inconsistency on the ATP Tour - and difficulties with his serve in specific - led to him exiting of the elite rankings and eventually parting ways with long-term mentor Cervara.
Currently working with Johansson and his other coach, the tennis star has gradually progressed in the last few weeks - climaxing in a closely contested 7-5 4-6 6-3 triumph over opponent Moutet.
It is the player's maiden championship since the Rome competition and maiden on a hard surface after that period of the previous year.
Success also means he has achieved 21 titles at twenty-one different tournaments.
"For the first time I have attended a event with my children together, so to secure a title is really nice," said ranked player Daniil Medvedev.
"This title is in tribute of my child Victoria, because the first title I got when my older daughter Alisa was born was for her."
Medvedev, the 2021 US Open champion, had failed in his past six championship matches, including in Halle in the past months.
The player's defensive strategy and frequent reactions on the playing surface had prompted some to question if his skill to play at the highest level was concluded.
Yet the player has implemented adjustments in recent weeks, attempting to advance forward and play aggressively, backed up by an improved serving game.
Medvedev recovered from a disadvantage in the first set against the difficult Moutet, securing four of the final five points to go ahead.
Both players traded service breaks in the following set before the challenger, attempting for his initial tour victory, took control to create a third set.
The opponent defended 4 early-game break points in a close deciding set before Medvedev secured a break to that score to close out the victory.
Suitably, Medvedev earned the title with a rally at the front of the court, with his opponent unable to manage a return after two hours and 38 minutes.