Nineteen of Medvedev's 21 titles have been earned on hardcourt
A revitalized Medvedev secured his maiden trophy for over two years with a win over Frenchman Moutet in the competition final.
Medvedev, a former top-ranked player, has endured a difficult period, managing just one match at the Grand Slams and undergoing a meltdown at the US Open.
The player's varied form on the professional circuit - and issues with his serve in particular - caused him dropping out of the elite rankings and eventually separating with former coach Gilles Cervara.
Currently working with his coach and his other coach, he has steadily advanced in the past month - culminating in a closely contested three-set triumph over challenger Corentin Moutet.
It is the player's maiden trophy after the Italian tournament and maiden on a hard court after spring of the previous year.
The win also signifies Medvedev has secured 21 championships at 21 different competitions.
"It's the first time I have attended a competition with my two daughters together, so to get a championship is particularly special," commented ranked player the champion.
"This title is in tribute of my younger daughter Victoria, because the first title I won when my child Alisa was born was for her."
Medvedev, the former major winner, had lost his previous six finals, comprising in that event in the past months.
Medvedev's counter-punching strategy and regular outbursts on the playing surface had led some to wonder if his capacity to play at the top level was over.
But the player has made changes in the last few weeks, striving to come to the net and play aggressively, backed up by an improved serve.
The champion came back from a break down in the opening set against the tricky opponent, winning 4 of the concluding five points to take the lead.
Both players swapped breaks in the middle set before the challenger, attempting for his initial professional championship, took control to create a decider.
Moutet rescued four early break points in a tight third set before Medvedev broke to 15 to secure the win.
Appropriately, the winner secured victory with a point at the front of the court, with his opponent unable to handle a shot after over two and a half hours.