Nineteen of Medvedev's 21 championships have been achieved on hard surfaces
A resurgent the Russian player won his first trophy for nearly 30 months with success over Frenchman Moutet in the Almaty Open title decider.
Medvedev, a former top-ranked player, has endured a torrid year, achieving just a single victory at the Grand Slams and undergoing a setback at the New York tournament.
His inconsistency on the tennis tour - and issues with his serving in especial - led to him dropping out of the top ten and finally separating with long-time mentor Cervara.
Currently working with his coach and his other coach, the tennis star has steadily progressed in the last few weeks - peaking in a closely contested three-set win over challenger Moutet.
This represents Medvedev's maiden trophy after the Italian tournament and first on a hard surface from that period of the previous year.
Victory also signifies he has won 21 victories at 21 different tournaments.
"For the first time I'm at a tournament with my children together, so to win a title is really nice," stated world number 14 Medvedev.
"This victory is in honour of my second daughter Victoria, because the initial championship I got when my first daughter my daughter was born was for her."
Medvedev, the 2021 US Open champion, had lost his last six championship matches, including in the German tournament previously this season.
His defensive strategy and regular emotional displays on the playing surface had caused commentators to wonder if his capacity to compete at the top level was finished.
Yet the player has made changes in recent weeks, making an effort to advance forward and play positively, reinforced by an enhanced service.
Medvedev fought back from a disadvantage in the first set against the tricky Moutet, winning 4 of the last five exchanges to gain the advantage.
The pair traded break points in the second set before the challenger, attempting for his maiden professional victory, seized the initiative to force a third set.
Moutet saved four early chances in a competitive third set before Medvedev secured a break to fifteen to secure the win.
Suitably, the winner secured the win with a rally at the net, with the Frenchman failing to handle a shot after a lengthy match.
