19 of Medvedev's 21 championships have been won on hard surfaces
A resurgent Medvedev secured his first trophy for 882 days with victory over opponent Moutet in the Almaty Open final.
Medvedev, a ex- number one, has had a difficult year, winning just a single victory at the Grand Slams and experiencing a difficult moment at the New York tournament.
The player's varied form on the ATP Tour - and difficulties with his serving in specific - caused him dropping out of the world's top 10 and ultimately parting ways with long-term mentor his previous coach.
Now working with Johansson and Rohan Goetzke, Medvedev has consistently progressed in the last few weeks - peaking in a closely contested three-set triumph over opponent Moutet.
It is Medvedev's first trophy following the Italian tournament and first on a hardcourt after that period of that year.
Victory also means he has secured 21 victories at twenty-one distinct tournaments.
"It's the first time I am participating in a event with my both daughters together, so to get a trophy is especially meaningful," commented tennis professional Medvedev.
"This victory is in tribute of my child Victoria, because the first title I achieved when my first daughter her name was born was for her."
Medvedev, the former major winner, had lost his previous six title deciders, comprising in Halle previously this season.
His retrieving strategy and frequent outbursts on the tennis court had prompted observers to doubt if his ability to play at the elite level was over.
Yet the 29-year-old has implemented adjustments in the last few weeks, striving to approach the net and play positively, backed up by an improved serve.
Medvedev recovered from a disadvantage in the initial set against the difficult Moutet, taking four of the final five points to gain the advantage.
Both players exchanged service breaks in the following set before the challenger, bidding for his initial ATP Tour championship, gained dominance to force a final set.
He rescued four early-game break points in a tight final set before Medvedev broke to 15 to secure the win.
Appropriately, he earned the title with a shot at the net, with the Frenchman unable to manage a volley after two hours and 38 minutes.