Nineteen of Medvedev's 21 championships have been earned on hard surfaces
A revitalized the Russian player won his maiden championship for nearly 30 months with victory over opponent Moutet in the Almaty Open title decider.
The Russian, a former top-ranked player, has endured a challenging season, managing just one win at the major tournaments and undergoing a difficult moment at the New York tournament.
Medvedev's unpredictability on the tennis tour - and struggles with his serve in particular - resulted in him exiting of the world's top 10 and finally separating with long-term mentor Cervara.
Currently working with Johansson and his other coach, the tennis star has consistently improved in the past month - culminating in a closely contested 7-5 4-6 6-3 triumph over Frenchman Moutet.
This represents Medvedev's first title since the Italian tournament and initial on a hard surface since that period of that year.
Victory also means he has secured 21 titles at twenty-one various competitions.
"It's the first time I'm at a competition with my children together, so to win a trophy is especially meaningful," said ranked player Medvedev.
"This victory is in dedication of my second daughter my daughter, because the initial championship I won when my child her name was delivered was for her."
The athlete, the past champion, had lost his previous six title deciders, including in the German tournament previously this season.
The player's retrieving play style and frequent reactions on court had prompted observers to wonder if his skill to play at the elite level was finished.
However the player has implemented adjustments in recent weeks, striving to advance forward and play assertively, supported by an improved service.
He fought back from a deficit in the first set against the challenging Frenchman, winning 4 of the final five games to go ahead.
The competitors traded service breaks in the following set before Moutet, attempting for his initial tour title, took control to push for a final set.
Moutet saved four early-game chances in a tight third set before Medvedev broke to 15 to secure the win.
Appropriately, the winner earned the win with a rally at the front of the court, with the Frenchman incapable to control a shot after over two and a half hours.