19 of the Russian's 21 titles have been won on hardcourt
A revitalized Medvedev claimed his initial title for nearly 30 months with a win over opponent Moutet in the Almaty Open title decider.
The Russian, a former number one, has endured a torrid year, achieving just one match at the Grand Slams and experiencing a setback at the American major.
The player's varied form on the tennis tour - and issues with his serving in specific - led to him dropping out of the world's top 10 and finally splitting with long-time coach Cervara.
Currently collaborating with Thomas Johansson and Rohan Goetzke, Medvedev has gradually progressed in the recent weeks - culminating in a hard-fought three-set victory over challenger Moutet.
This marks the player's first championship since the Rome competition and maiden on a hardcourt since March of the previous year.
Success also signifies the Russian has achieved twenty-one victories at twenty-one various events.
"For the first time I have attended a competition with my two daughters simultaneously, so to win a title is particularly special," commented world number 14 Medvedev.
"This title is in dedication of my younger daughter Victoria, because the maiden victory I achieved when my child my daughter was delivered was for her."
The athlete, the past champion, had failed in his last six finals, including in that event earlier this year.
The player's retrieving strategy and regular reactions on the playing surface had caused observers to doubt if his capacity to compete at the elite level was over.
But the athlete has implemented adjustments in the last few weeks, making an effort to come to the net and perform assertively, backed up by an improved serving game.
The champion recovered from a deficit in the opening set against the difficult opponent, taking 4 of the last five exchanges to gain the advantage.
Both players exchanged service breaks in the following set before the challenger, bidding for his maiden ATP Tour victory, seized the initiative to push for a decider.
He saved 4 early-game chances in a close third set before the champion broke to that score to close out the victory.
Fittingly, the winner earned the title with a shot at the front of the court, with the Frenchman failing to handle a volley after a lengthy match.