Nineteen of Medvedev's 21 championships have been won on hard surfaces
A resurgent Medvedev secured his initial championship for over two years with success over Frenchman Moutet in the competition championship match.
The Russian, a ex- top-ranked player, has had a difficult period, achieving just a single victory at the major tournaments and experiencing a setback at the US Open.
His inconsistency on the professional circuit - and struggles with his service game in specific - resulted in him falling of the elite rankings and eventually splitting with long-time coach Gilles Cervara.
Now working with Thomas Johansson and Goetzke, he has consistently advanced in the past month - climaxing in a closely contested competitive victory over opponent Moutet.
It is his initial title since the Rome competition and initial on a hardcourt since March of 2023.
Success also means he has won 21 championships at 21 different competitions.
"For the first time I have attended a competition with my children together, so to win a title is particularly special," said world number 14 the champion.
"This victory is in honour of my child Victoria, because the first title I achieved when my older daughter my daughter was born was for her."
The tennis star, the past champion, had lost his previous six title deciders, featuring in that event in the past months.
His defensive approach and recurring reactions on the tennis court had prompted commentators to doubt if his ability to compete at the top level was over.
But the player has altered his approach in recent weeks, attempting to approach the net and perform positively, backed up by an better service.
Medvedev fought back from a break down in the first set against the tricky opponent, winning 4 of the final five exchanges to take the lead.
The competitors swapped breaks in the second set before the challenger, striving for his first tour title, seized the initiative to create a final set.
Moutet rescued 4 early-game break points in a tight final set before Medvedev secured a break to fifteen to secure the win.
Fittingly, the winner earned victory with a point at the front of the court, with Moutet failing to manage a volley after a lengthy match.