Nineteen of Medvedev's twenty-one championships have been achieved on hard surfaces
A revitalized the Russian player secured his first championship for 882 days with victory over Frenchman Moutet in the tournament title decider.
The Russian, a ex- world number one, has had a torrid year, winning just one win at the big events and undergoing a setback at the New York tournament.
Medvedev's inconsistency on the ATP Tour - and issues with his serve in especial - led to him dropping out of the world's top 10 and ultimately splitting with long-time mentor Gilles Cervara.
Now collaborating with Johansson and Goetzke, the tennis star has steadily improved in the last few weeks - peaking in a hard-fought 7-5 4-6 6-3 triumph over challenger Moutet.
It is the player's first trophy since the 2023 Rome Masters and first on a hardcourt from that period of that year.
Victory also signifies the Russian has achieved 21 championships at 21 distinct competitions.
"This marks the first occasion I have attended a competition with my both daughters simultaneously, so to get a championship is especially meaningful," commented world number 14 the champion.
"This victory is in honour of my second daughter her name, because the first title I won when my first daughter Alisa was born was for her."
The tennis star, the former major winner, had been defeated in his previous six finals, including in the German tournament previously this season.
Medvedev's counter-punching play style and frequent emotional displays on court had caused some to wonder if his ability to play at the highest level was finished.
Yet the player has implemented adjustments in the past month, striving to come to the net and perform aggressively, backed up by an enhanced service.
The champion came back from a break down in the first set against the tricky Frenchman, winning four of the concluding five points to take the lead.
The competitors traded service breaks in the following set before Moutet, attempting for his first ATP Tour championship, took control to push for a final set.
Moutet saved 4 initial chances in a competitive third set before the champion broke to that score to close out the victory.
Suitably, Medvedev earned the title with a shot at the net area, with the Frenchman incapable to manage a return after a lengthy match.