Nineteen of Medvedev's 21 championships have been earned on hardcourt
A revitalized the Russian player claimed his maiden title for 882 days with success over opponent Moutet in the tournament title decider.
The Russian, a ex- number one, has endured a challenging year, achieving just one match at the major tournaments and suffering a setback at the New York tournament.
The player's unpredictability on the professional circuit - and difficulties with his serve in particular - caused him exiting of the world's top 10 and eventually splitting with long-term coach Gilles Cervara.
Currently collaborating with Thomas Johansson and Goetzke, the tennis star has steadily advanced in the past month - climaxing in a hard-fought three-set triumph over Frenchman Moutet.
It is Medvedev's maiden trophy after the Rome competition and first on a hardcourt from that period of 2023.
Success also indicates the Russian has secured twenty-one victories at twenty-one distinct competitions.
"This marks the first occasion I am participating in a event with my children at once, so to secure a trophy is especially meaningful," commented world number 14 the champion.
"This title is in dedication of my child Victoria, because the initial championship I achieved when my child her name was born was for her."
The tennis star, the past champion, had lost his past six championship matches, featuring in Halle earlier this year.
Medvedev's counter-punching approach and recurring reactions on the tennis court had prompted commentators to wonder if his skill to compete at the highest level was over.
Yet the player has altered his approach in the last few weeks, attempting to approach the net and play assertively, reinforced by an enhanced service.
He came back from a deficit in the opening set against the difficult opponent, securing 4 of the concluding five games to take the lead.
Both players traded break points in the second set before the challenger, attempting for his initial professional championship, gained dominance to force a decider.
Moutet saved 4 early-game chances in a competitive third set before the champion secured a break to 15 to serve for the match.
Fittingly, Medvedev secured the title with a point at the front of the court, with his opponent failing to control a volley after a lengthy match.