Nineteen of Medvedev's 21 titles have been won on hard courts
A comeback the Russian player secured his first title for nearly 30 months with success over opponent Moutet in the Almaty Open final.
Medvedev, a former top-ranked player, has endured a challenging season, winning just a single victory at the major tournaments and experiencing a meltdown at the US Open.
Medvedev's varied form on the tennis tour - and difficulties with his serving in particular - caused him dropping out of the elite rankings and finally splitting with long-term trainer Cervara.
Currently training with Thomas Johansson and his other coach, Medvedev has steadily progressed in the last few weeks - culminating in a tightly fought 7-5 4-6 6-3 triumph over opponent Corentin Moutet.
It is Medvedev's maiden championship after the Italian tournament and maiden on a hardcourt since that period of the previous year.
Success also signifies the Russian has achieved 21 titles at twenty-one various events.
"For the first time I have attended a event with my both daughters together, so to win a championship is particularly special," commented world number 14 Medvedev.
"This championship is in dedication of my child her name, because the first title I won when my first daughter her name was born was for her."
Medvedev, the past champion, had been defeated in his past six championship matches, including in the German tournament previously this season.
His retrieving approach and recurring emotional displays on the tennis court had led commentators to wonder if his ability to perform at the highest level was finished.
However the 29-year-old has made changes in the past month, striving to come to the net and compete aggressively, backed up by an improved service.
Medvedev came back from a disadvantage in the opening set against the tricky opponent, taking four of the last five games to gain the advantage.
The competitors traded service breaks in the middle set before the challenger, bidding for his maiden tour championship, seized the initiative to push for a decider.
He saved 4 early chances in a close deciding set before the champion secured a break to that score to close out the victory.
Fittingly, the winner clinched the win with a rally at the front of the court, with Moutet incapable to control a return after two hours and 38 minutes.
