Nineteen of the Russian's 21 victories have been won on hard surfaces
A revitalized Medvedev claimed his first championship for nearly 30 months with a win over opponent Moutet in the tournament final.
The Russian, a ex- number one, has endured a challenging year, managing just one match at the Grand Slams and undergoing a setback at the American major.
The player's inconsistency on the tennis tour - and struggles with his serve in specific - caused him exiting of the world's top 10 and ultimately splitting with long-term mentor Gilles Cervara.
Currently working with Thomas Johansson and Rohan Goetzke, Medvedev has gradually progressed in the past month - culminating in a hard-fought three-set win over Frenchman Moutet.
This marks his initial trophy following the Italian tournament and initial on a hard court from March of that year.
Victory also indicates the Russian has won 21 titles at twenty-one different events.
"This marks the first occasion I have attended a tournament with my two daughters at once, so to win a championship is really nice," stated world number 14 the champion.
"This championship is in dedication of my second daughter her name, because the first title I won when my first daughter her name was delivered was for her."
Medvedev, the former major winner, had lost his last six championship matches, featuring in that event in the past months.
Medvedev's counter-punching play style and frequent emotional displays on the playing surface had prompted commentators to question if his capacity to play at the top level was over.
But the athlete has made changes in the last few weeks, attempting to advance forward and play assertively, reinforced by an better serve.
He recovered from a break down in the first set against the challenging opponent, winning four of the final five games to gain the advantage.
The competitors traded break points in the second set before Moutet, striving for his first ATP Tour title, gained dominance to push for a decider.
The opponent defended 4 early-game break points in a close deciding set before Medvedev broke to 15 to serve for the match.
Appropriately, the winner earned the title with a rally at the net area, with Moutet incapable to handle a return after over two and a half hours.
