19 of the Russian's 21 championships have been earned on hard courts
A revitalized Medvedev claimed his initial championship for nearly 30 months with a win over Frenchman Moutet in the competition final.
Medvedev, a former number one, has experienced a difficult year, achieving just a single victory at the big events and undergoing a setback at the US Open.
The player's unpredictability on the professional circuit - and struggles with his serving in particular - led to him dropping out of the top ten and eventually splitting with long-time trainer Cervara.
Currently training with his coach and Goetzke, Medvedev has gradually improved in the recent weeks - peaking in a hard-fought three-set triumph over opponent Moutet.
This marks Medvedev's initial title since the Rome competition and first on a hardcourt after March of 2023.
The win also indicates the Russian has achieved 21 victories at twenty-one various competitions.
"It's the first time I'm at a competition with my children simultaneously, so to secure a title is really nice," said tennis professional Medvedev.
"This victory is in tribute of my younger daughter my daughter, because the first title I won when my child her name was born was for her."
The tennis star, the past champion, had failed in his previous six championship matches, featuring in Halle earlier this year.
His counter-punching strategy and recurring emotional displays on court had caused observers to question if his skill to play at the highest level was concluded.
However the 29-year-old has made changes in recent weeks, striving to advance forward and perform aggressively, supported by an enhanced serve.
The champion recovered from a deficit in the initial set against the challenging opponent, securing 4 of the final five points to go ahead.
Both players swapped service breaks in the following set before Moutet, striving for his maiden ATP Tour victory, gained dominance to push for a third set.
He defended four initial chances in a tight deciding set before Medvedev secured a break to 15 to secure the win.
Suitably, the winner earned victory with a rally at the net, with the Frenchman unable to handle a shot after two hours and 38 minutes.