19 of the Russian's 21 titles have been earned on hardcourt
A comeback the Russian player won his first championship for 882 days with success over opponent Moutet in the Almaty Open title decider.
The Russian, a former top-ranked player, has experienced a difficult year, winning just a single victory at the Grand Slams and experiencing a setback at the New York tournament.
The player's inconsistency on the ATP Tour - and struggles with his serve in especial - caused him dropping out of the elite rankings and ultimately separating with long-term mentor Gilles Cervara.
Currently training with Thomas Johansson and Rohan Goetzke, Medvedev has steadily progressed in the recent weeks - peaking in a tightly fought competitive win over Frenchman Moutet.
This represents his maiden title after the Italian tournament and first on a hardcourt since spring of the previous year.
Success also signifies the Russian has secured twenty-one titles at 21 distinct events.
"For the first time I am participating in a tournament with my children together, so to secure a championship is especially meaningful," stated ranked player Medvedev.
"This title is in honour of my child my daughter, because the maiden victory I achieved when my older daughter Alisa was born was for her."
Medvedev, the former major winner, had failed in his last six title deciders, featuring in that event in the past months.
His defensive play style and recurring outbursts on court had prompted commentators to doubt if his capacity to play at the elite level was over.
However the player has altered his approach in the last few weeks, making an effort to come to the net and compete aggressively, supported by an improved serving game.
The champion fought back from a deficit in the initial set against the tricky Moutet, winning 4 of the concluding five points to take the lead.
The pair swapped break points in the following set before the Frenchman, striving for his maiden tour title, seized the initiative to force a third set.
He rescued 4 initial opportunities in a tight deciding set before the Russian secured a break to that score to serve for the match.
Fittingly, the winner earned the win with a point at the net, with Moutet incapable to handle a volley after a lengthy match.