Nineteen of Medvedev's 21 victories have been won on hard courts
A resurgent the Russian player secured his initial championship for nearly 30 months with victory over Frenchman Moutet in the Almaty Open championship match.
Medvedev, a ex- world number one, has experienced a torrid year, achieving just a single victory at the big events and experiencing a meltdown at the American major.
Medvedev's varied form on the ATP Tour - and struggles with his service game in specific - resulted in him exiting of the world's top 10 and ultimately parting ways with long-time mentor his previous coach.
Currently training with Thomas Johansson and Rohan Goetzke, Medvedev has consistently advanced in the past month - climaxing in a tightly fought 7-5 4-6 6-3 win over opponent Corentin Moutet.
This represents Medvedev's first title following the Rome competition and initial on a hardcourt after spring of that year.
Victory also indicates he has secured 21 titles at twenty-one different tournaments.
"It's the first time I am participating in a event with my two daughters together, so to win a trophy is really nice," commented ranked player Medvedev.
"This championship is in honour of my younger daughter my daughter, because the maiden victory I won when my older daughter her name was born was for her."
The tennis star, the past champion, had been defeated in his last six championship matches, including in Halle in the past months.
Medvedev's defensive strategy and regular emotional displays on the tennis court had led commentators to question if his ability to play at the top level was concluded.
Yet the player has made changes in the last few weeks, attempting to advance forward and compete aggressively, reinforced by an better service.
He came back from a deficit in the first set against the tricky Frenchman, taking four of the last five exchanges to gain the advantage.
The pair traded service breaks in the second set before the Frenchman, bidding for his first professional victory, gained dominance to create a decider.
He saved four early chances in a competitive deciding set before Medvedev won the break to that score to close out the victory.
Fittingly, he secured the win with a rally at the net area, with Moutet failing to control a volley after over two and a half hours.
