Nineteen of Medvedev's twenty-one championships have been earned on hard surfaces
A resurgent the Russian player won his maiden title for 882 days with victory over Frenchman Moutet in the competition final.
The athlete, a former number one, has endured a torrid season, managing just a single victory at the major tournaments and undergoing a difficult moment at the US Open.
The player's unpredictability on the ATP Tour - and issues with his serve in especial - led to him dropping out of the elite rankings and ultimately separating with former trainer his previous coach.
Now collaborating with Johansson and Goetzke, the tennis star has consistently advanced in the past month - peaking in a tightly fought 7-5 4-6 6-3 triumph over Frenchman Moutet.
This represents the player's first trophy following the Rome competition and initial on a hardcourt after that period of 2023.
Success also indicates the Russian has won 21 titles at 21 distinct tournaments.
"This marks the first occasion I am participating in a event with my both daughters simultaneously, so to get a title is especially meaningful," stated world number 14 Medvedev.
"This championship is in tribute of my child her name, because the maiden victory I got when my first daughter Alisa was born was for her."
The athlete, the past champion, had been defeated in his last six finals, featuring in that event earlier this year.
Medvedev's retrieving approach and recurring emotional displays on the tennis court had caused commentators to doubt if his ability to perform at the highest level was concluded.
But the player has made changes in the past month, making an effort to come to the net and play positively, reinforced by an improved serve.
Medvedev fought back from a deficit in the initial set against the difficult Frenchman, taking four of the final five exchanges to go ahead.
The pair traded break points in the following set before the challenger, attempting for his first tour victory, gained dominance to push for a decider.
He rescued 4 early chances in a competitive deciding set before the Russian secured a break to fifteen to close out the victory.
Appropriately, Medvedev earned victory with a point at the front of the court, with his opponent failing to manage a return after a lengthy match.