19 of the Russian's twenty-one titles have been won on hard courts
A resurgent Medvedev claimed his first championship for nearly 30 months with success over Frenchman Moutet in the tournament final.
Medvedev, a ex- number one, has experienced a difficult year, winning just a single victory at the major tournaments and experiencing a setback at the US Open.
Medvedev's unpredictability on the ATP Tour - and struggles with his service game in specific - resulted in him dropping out of the elite rankings and eventually separating with long-term mentor Gilles Cervara.
Now working with Thomas Johansson and his other coach, he has gradually improved in the last few weeks - climaxing in a hard-fought three-set win over opponent Moutet.
It is his initial championship following the Rome competition and first on a hard surface after that period of 2023.
Victory also signifies he has won 21 victories at twenty-one different competitions.
"This marks the first occasion I'm at a tournament with my both daughters together, so to get a title is especially meaningful," said ranked player the champion.
"This title is in tribute of my second daughter my daughter, because the maiden victory I got when my child Alisa was born was for her."
The athlete, the former major winner, had been defeated in his previous six championship matches, including in Halle in the past months.
His defensive play style and regular emotional displays on court had led commentators to doubt if his skill to compete at the highest level was concluded.
But the athlete has implemented adjustments in the past month, making an effort to approach the net and play positively, supported by an improved serve.
He came back from a disadvantage in the opening set against the difficult opponent, winning 4 of the last five games to go ahead.
The pair swapped service breaks in the middle set before Moutet, bidding for his maiden tour victory, seized the initiative to force a third set.
Moutet saved four initial opportunities in a tight deciding set before the Russian broke to 15 to serve for the match.
Appropriately, he earned victory with a rally at the net area, with Moutet failing to manage a shot after over two and a half hours.