19 of Medvedev's 21 victories have been achieved on hardcourt
A comeback the Russian player secured his first trophy for over two years with success over opponent Moutet in the Almaty Open title decider.
Medvedev, a former number one, has had a torrid period, managing just one match at the big events and undergoing a meltdown at the New York tournament.
Medvedev's varied form on the ATP Tour - and struggles with his serving in particular - resulted in him falling of the world's top 10 and ultimately separating with former mentor Gilles Cervara.
Currently training with his coach and Rohan Goetzke, Medvedev has steadily progressed in the last few weeks - culminating in a hard-fought competitive victory over Frenchman Moutet.
This represents the player's maiden championship since the Italian tournament and first on a hardcourt from March of that year.
Victory also indicates Medvedev has achieved 21 victories at 21 different tournaments.
"This marks the first occasion I am participating in a tournament with my both daughters together, so to win a trophy is especially meaningful," said ranked player Medvedev.
"This title is in tribute of my child my daughter, because the maiden victory I achieved when my older daughter my daughter was born was for her."
The athlete, the former major winner, had lost his past six title deciders, featuring in that event previously this season.
His defensive strategy and recurring emotional displays on the playing surface had prompted commentators to wonder if his ability to compete at the top level was finished.
But the player has made changes in the past month, making an effort to approach the net and compete aggressively, supported by an improved serving game.
He fought back from a break down in the initial set against the difficult Frenchman, securing four of the last five exchanges to go ahead.
Both players exchanged break points in the following set before the Frenchman, striving for his first ATP Tour title, gained dominance to force a final set.
Moutet rescued 4 initial chances in a tight third set before the Russian secured a break to fifteen to serve for the match.
Fittingly, he secured the title with a rally at the net area, with Moutet incapable to manage a shot after a lengthy match.
