Nineteen of the Russian's 21 titles have been earned on hardcourt
A comeback Medvedev won his initial trophy for 882 days with a win over opponent Moutet in the Almaty Open title decider.
The athlete, a ex- top-ranked player, has experienced a challenging season, achieving just one win at the Grand Slams and suffering a setback at the New York tournament.
His unpredictability on the ATP Tour - and issues with his service game in especial - led to him dropping out of the elite rankings and eventually parting ways with long-time trainer Gilles Cervara.
Now training with Johansson and Rohan Goetzke, the tennis star has steadily improved in the last few weeks - climaxing in a closely contested three-set victory over opponent Moutet.
This marks Medvedev's maiden championship following the Italian tournament and first on a hardcourt since March of the previous year.
The win also signifies the Russian has secured twenty-one victories at 21 distinct competitions.
"It's the first time I'm at a competition with my two daughters together, so to secure a championship is particularly special," said world number 14 Medvedev.
"This title is in dedication of my second daughter Victoria, because the initial championship I achieved when my child my daughter was born was for her."
Medvedev, the former major winner, had been defeated in his last six finals, featuring in the German tournament earlier this year.
The player's counter-punching play style and recurring outbursts on the tennis court had caused observers to wonder if his skill to perform at the elite level was finished.
Yet the 29-year-old has implemented adjustments in the past month, attempting to advance forward and perform aggressively, backed up by an improved serving game.
He fought back from a disadvantage in the opening set against the difficult Moutet, securing 4 of the last five exchanges to take the lead.
The competitors exchanged break points in the middle set before Moutet, striving for his first ATP Tour championship, took control to force a decider.
He defended 4 early chances in a competitive deciding set before the champion broke to 15 to secure the win.
Fittingly, the winner earned the title with a rally at the net, with his opponent incapable to manage a shot after a lengthy match.
