19 of Medvedev's 21 championships have been achieved on hardcourt
A comeback the Russian player claimed his initial title for 882 days with a win over Frenchman Moutet in the competition championship match.
The athlete, a ex- number one, has endured a torrid year, managing just one win at the big events and suffering a meltdown at the US Open.
The player's inconsistency on the professional circuit - and struggles with his serve in specific - caused him falling of the world's top 10 and finally parting ways with former mentor Gilles Cervara.
Presently working with Johansson and his other coach, Medvedev has gradually advanced in the recent weeks - peaking in a closely contested competitive triumph over challenger Moutet.
It is the player's maiden championship after the Rome competition and first on a hardcourt after March of the previous year.
Success also signifies Medvedev has achieved twenty-one titles at twenty-one various tournaments.
"For the first time I am participating in a tournament with my both daughters simultaneously, so to get a trophy is really nice," commented world number 14 Medvedev.
"This championship is in honour of my child her name, because the initial championship I got when my child Alisa was born was for her."
The athlete, the 2021 US Open champion, had failed in his past six finals, comprising in the German tournament earlier this year.
His defensive play style and frequent outbursts on the tennis court had caused some to question if his skill to compete at the highest level was finished.
But the player has made changes in recent weeks, striving to advance forward and compete aggressively, supported by an enhanced service.
Medvedev fought back from a disadvantage in the initial set against the tricky Moutet, taking four of the last five exchanges to gain the advantage.
Both players swapped service breaks in the second set before the Frenchman, attempting for his initial tour victory, seized the initiative to create a third set.
Moutet rescued four early opportunities in a competitive final set before Medvedev won the break to fifteen to serve for the match.
Appropriately, he secured the win with a rally at the front of the court, with Moutet incapable to manage a volley after two hours and 38 minutes.