19 of the Russian's 21 victories have been earned on hard courts
A resurgent the Russian player claimed his first championship for 882 days with success over Frenchman Moutet in the Almaty Open title decider.
The Russian, a former top-ranked player, has experienced a torrid year, winning just one match at the major tournaments and experiencing a difficult moment at the US Open.
The player's unpredictability on the ATP Tour - and issues with his service game in specific - led to him falling of the elite rankings and eventually splitting with former coach his previous coach.
Presently working with Thomas Johansson and Goetzke, the tennis star has consistently improved in the last few weeks - culminating in a hard-fought 7-5 4-6 6-3 victory over opponent Moutet.
This marks his first title since the Italian tournament and initial on a hard court from spring of the previous year.
The win also means Medvedev has secured twenty-one victories at twenty-one different competitions.
"It's the first time I'm at a tournament with my two daughters simultaneously, so to win a title is especially meaningful," said world number 14 the champion.
"This title is in honour of my child her name, because the initial championship I achieved when my child her name was delivered was for her."
The tennis star, the past champion, had been defeated in his past six title deciders, comprising in Halle earlier this year.
His counter-punching approach and regular reactions on the tennis court had prompted commentators to wonder if his ability to compete at the highest level was over.
Yet the 29-year-old has made changes in the past month, attempting to come to the net and compete aggressively, backed up by an enhanced serving game.
Medvedev recovered from a break down in the initial set against the difficult Frenchman, winning 4 of the last five games to gain the advantage.
Both players traded breaks in the second set before Moutet, bidding for his initial ATP Tour championship, took control to force a third set.
He saved four initial break points in a close third set before the Russian secured a break to that score to secure the win.
Fittingly, Medvedev earned the win with a point at the net area, with the Frenchman incapable to control a volley after a lengthy match.