19 of Medvedev's 21 victories have been won on hard surfaces
A resurgent the Russian player won his first title for over two years with victory over opponent Moutet in the Almaty Open title decider.
The Russian, a ex- world number one, has experienced a challenging period, achieving just one match at the major tournaments and suffering a difficult moment at the New York tournament.
His unpredictability on the professional circuit - and struggles with his serving in specific - resulted in him falling of the elite rankings and finally splitting with former coach Gilles Cervara.
Now training with Johansson and Goetzke, he has steadily improved in the recent weeks - peaking in a tightly fought competitive win over Frenchman Moutet.
This represents the player's maiden title following the 2023 Rome Masters and first on a hardcourt after spring of the previous year.
Victory also signifies the Russian has secured twenty-one titles at twenty-one distinct events.
"It's the first time I have attended a event with my children together, so to get a championship is particularly special," commented ranked player the champion.
"This victory is in honour of my second daughter my daughter, because the maiden victory I got when my older daughter Alisa was born was for her."
Medvedev, the 2021 US Open champion, had lost his previous six championship matches, comprising in the German tournament previously this season.
Medvedev's counter-punching play style and regular emotional displays on the tennis court had caused commentators to doubt if his capacity to perform at the highest level was over.
Yet the 29-year-old has made changes in the past month, striving to advance forward and play aggressively, reinforced by an enhanced service.
Medvedev recovered from a break down in the initial set against the challenging Moutet, winning 4 of the last five exchanges to take the lead.
The pair swapped service breaks in the middle set before Moutet, attempting for his maiden tour title, seized the initiative to create a decider.
Moutet defended four initial opportunities in a tight third set before the champion secured a break to that score to close out the victory.
Suitably, Medvedev clinched the title with a point at the net area, with his opponent failing to control a shot after a lengthy match.