19 of the Russian's 21 titles have been achieved on hard courts
A comeback Medvedev secured his initial trophy for nearly 30 months with a win over Frenchman Moutet in the competition championship match.
Medvedev, a former world number one, has had a torrid period, managing just one win at the big events and experiencing a meltdown at the American major.
His inconsistency on the ATP Tour - and issues with his service game in particular - resulted in him exiting of the top ten and finally parting ways with long-term coach Gilles Cervara.
Now training with Johansson and Goetzke, the tennis star has steadily progressed in the past month - culminating in a tightly fought 7-5 4-6 6-3 victory over opponent Moutet.
This marks the player's initial trophy after the 2023 Rome Masters and first on a hard court since spring of 2023.
Victory also signifies the Russian has won twenty-one championships at 21 different tournaments.
"It's the first time I have attended a competition with my both daughters simultaneously, so to win a trophy is really nice," said ranked player the champion.
"This title is in dedication of my child her name, because the initial championship I got when my child Alisa was born was for her."
The tennis star, the 2021 US Open champion, had been defeated in his past six championship matches, comprising in the German tournament in the past months.
His retrieving strategy and regular emotional displays on the tennis court had led observers to doubt if his skill to compete at the highest level was over.
But the athlete has implemented adjustments in recent weeks, striving to advance forward and play assertively, supported by an improved serving game.
He recovered from a disadvantage in the opening set against the challenging Moutet, winning 4 of the final five points to go ahead.
The pair traded service breaks in the following set before the Frenchman, bidding for his maiden professional title, gained dominance to force a final set.
Moutet saved 4 early break points in a competitive deciding set before the Russian won the break to 15 to serve for the match.
Fittingly, the winner clinched victory with a point at the net, with the Frenchman failing to manage a shot after over two and a half hours.