Nineteen of Medvedev's 21 victories have been earned on hard surfaces
A resurgent Medvedev claimed his maiden title for 882 days with a win over opponent Moutet in the competition final.
The athlete, a former number one, has had a challenging period, managing just one win at the Grand Slams and experiencing a difficult moment at the American major.
His inconsistency on the tennis tour - and difficulties with his serve in especial - resulted in him falling of the world's top 10 and eventually parting ways with long-term trainer Gilles Cervara.
Currently training with Thomas Johansson and Rohan Goetzke, he has steadily improved in the past month - climaxing in a hard-fought competitive victory over opponent Moutet.
This represents his first trophy following the Rome competition and first on a hard court after that period of that year.
Success also means Medvedev has achieved 21 titles at twenty-one distinct tournaments.
"For the first time I'm at a competition with my children together, so to get a title is particularly special," said tennis professional Medvedev.
"This title is in honour of my child her name, because the initial championship I achieved when my older daughter her name was born was for her."
Medvedev, the 2021 US Open champion, had lost his past six title deciders, including in that event previously this season.
The player's counter-punching play style and recurring reactions on the tennis court had prompted commentators to doubt if his ability to play at the elite level was finished.
However the 29-year-old has implemented adjustments in the last few weeks, making an effort to advance forward and play assertively, backed up by an improved serve.
Medvedev came back from a disadvantage in the opening set against the tricky opponent, securing 4 of the last five points to take the lead.
The pair swapped break points in the middle set before Moutet, striving for his first tour championship, gained dominance to force a final set.
The opponent rescued 4 early break points in a close deciding set before the champion secured a break to 15 to secure the win.
Fittingly, Medvedev secured victory with a shot at the net area, with his opponent unable to handle a return after over two and a half hours.