19 of the Russian's 21 victories have been earned on hard courts
A resurgent the Russian player claimed his initial trophy for 882 days with success over Frenchman Moutet in the Almaty Open title decider.
The Russian, a ex- number one, has endured a torrid season, achieving just one match at the big events and undergoing a setback at the US Open.
His varied form on the tennis tour - and difficulties with his serving in particular - caused him falling of the world's top 10 and eventually splitting with former coach his previous coach.
Now working with Thomas Johansson and his other coach, the tennis star has gradually improved in the last few weeks - culminating in a hard-fought competitive triumph over Frenchman Moutet.
This marks Medvedev's first championship since the Italian tournament and initial on a hard surface from spring of that year.
Victory also means the Russian has secured 21 victories at 21 various competitions.
"This marks the first occasion I have attended a event with my children at once, so to secure a trophy is particularly special," commented world number 14 Medvedev.
"This victory is in dedication of my younger daughter Victoria, because the first title I won when my child her name was born was for her."
The tennis star, the former major winner, had been defeated in his past six title deciders, comprising in the German tournament earlier this year.
His counter-punching approach and regular reactions on the tennis court had led some to wonder if his skill to play at the highest level was over.
But the athlete has altered his approach in the past month, making an effort to advance forward and compete aggressively, reinforced by an improved serve.
Medvedev fought back from a break down in the first set against the challenging Moutet, taking four of the last five points to go ahead.
The pair traded break points in the middle set before Moutet, striving for his first ATP Tour championship, took control to create a final set.
The opponent rescued 4 initial opportunities in a tight final set before the Russian broke to 15 to secure the win.
Appropriately, Medvedev earned the win with a shot at the front of the court, with the Frenchman incapable to control a volley after a lengthy match.
