Nineteen of Medvedev's 21 victories have been achieved on hard surfaces
A comeback the Russian player won his first championship for nearly 30 months with success over Frenchman Moutet in the competition final.
Medvedev, a ex- world number one, has endured a difficult period, achieving just one win at the Grand Slams and experiencing a setback at the US Open.
His unpredictability on the ATP Tour - and struggles with his serving in especial - resulted in him exiting of the world's top 10 and ultimately separating with former mentor Gilles Cervara.
Currently training with his coach and Goetzke, he has steadily progressed in the last few weeks - peaking in a tightly fought 7-5 4-6 6-3 triumph over opponent Moutet.
This marks the player's initial trophy after the Rome competition and first on a hard surface since that period of that year.
The win also signifies the Russian has secured 21 championships at twenty-one various events.
"For the first time I am participating in a event with my children simultaneously, so to win a title is especially meaningful," said world number 14 Daniil Medvedev.
"This championship is in dedication of my child her name, because the first title I achieved when my child my daughter was born was for her."
Medvedev, the past champion, had lost his previous six title deciders, including in the German tournament earlier this year.
Medvedev's counter-punching strategy and regular emotional displays on court had led observers to question if his skill to compete at the elite level was finished.
However the player has made changes in the last few weeks, making an effort to come to the net and play positively, reinforced by an improved service.
He fought back from a disadvantage in the initial set against the difficult Moutet, taking four of the last five points to gain the advantage.
The competitors exchanged breaks in the second set before the Frenchman, attempting for his first professional victory, gained dominance to force a decider.
Moutet rescued four initial break points in a close third set before the Russian secured a break to 15 to secure the win.
Suitably, he secured the title with a shot at the front of the court, with his opponent failing to manage a return after a lengthy match.
