Nineteen of Medvedev's twenty-one titles have been won on hard courts
A comeback the Russian player won his initial title for 882 days with success over opponent Moutet in the competition final.
Medvedev, a former world number one, has had a challenging year, achieving just one win at the big events and experiencing a setback at the New York tournament.
Medvedev's inconsistency on the professional circuit - and issues with his serving in particular - led to him exiting of the elite rankings and finally separating with former coach Cervara.
Presently working with his coach and Goetzke, Medvedev has gradually improved in the recent weeks - climaxing in a tightly fought 7-5 4-6 6-3 triumph over Frenchman Moutet.
It is the player's maiden title following the Italian tournament and initial on a hard surface after that period of that year.
Success also signifies Medvedev has secured 21 titles at twenty-one distinct competitions.
"For the first time I have attended a competition with my children at once, so to get a trophy is particularly special," said world number 14 Daniil Medvedev.
"This title is in dedication of my child her name, because the first title I achieved when my older daughter her name was born was for her."
Medvedev, the former major winner, had lost his past six title deciders, comprising in the German tournament earlier this year.
The player's retrieving strategy and regular reactions on the playing surface had caused observers to doubt if his ability to perform at the elite level was over.
But the player has altered his approach in the last few weeks, striving to advance forward and perform positively, supported by an enhanced serve.
He fought back from a deficit in the first set against the challenging Frenchman, winning 4 of the concluding five exchanges to go ahead.
The pair swapped break points in the middle set before the Frenchman, bidding for his maiden tour victory, seized the initiative to create a decider.
Moutet defended four initial opportunities in a tight final set before the Russian broke to 15 to close out the victory.
Appropriately, Medvedev earned the win with a rally at the net area, with Moutet failing to handle a shot after two hours and 38 minutes.
