Nineteen of the Russian's 21 championships have been won on hard surfaces
A resurgent Medvedev claimed his initial trophy for over two years with a win over Frenchman Moutet in the tournament championship match.
The Russian, a former number one, has endured a difficult period, winning just a single victory at the major tournaments and experiencing a difficult moment at the US Open.
Medvedev's unpredictability on the ATP Tour - and difficulties with his service game in especial - caused him exiting of the world's top 10 and finally separating with former trainer Cervara.
Now training with Thomas Johansson and Goetzke, he has consistently advanced in the past month - climaxing in a hard-fought competitive victory over Frenchman Moutet.
It is his maiden championship since the Italian tournament and initial on a hardcourt since March of 2023.
Victory also signifies the Russian has achieved 21 victories at twenty-one distinct events.
"It's the first time I have attended a tournament with my children at once, so to win a championship is really nice," commented world number 14 the champion.
"This victory is in honour of my second daughter Victoria, because the maiden victory I achieved when my older daughter Alisa was delivered was for her."
The athlete, the former major winner, had been defeated in his past six title deciders, comprising in the German tournament earlier this year.
Medvedev's defensive approach and recurring reactions on court had led commentators to question if his ability to compete at the top level was finished.
However the player has implemented adjustments in the past month, striving to advance forward and play aggressively, backed up by an improved serving game.
He came back from a disadvantage in the opening set against the challenging opponent, taking 4 of the concluding five points to take the lead.
The pair exchanged break points in the following set before the Frenchman, attempting for his first tour championship, took control to push for a decider.
The opponent saved four early chances in a competitive final set before the Russian broke to 15 to serve for the match.
Suitably, he clinched the title with a rally at the front of the court, with the Frenchman incapable to handle a volley after over two and a half hours.