19 of the Russian's 21 victories have been won on hard courts
A comeback Medvedev secured his initial championship for nearly 30 months with success over Frenchman Moutet in the competition title decider.
The Russian, a ex- number one, has experienced a challenging season, achieving just a single victory at the big events and experiencing a setback at the New York tournament.
Medvedev's varied form on the professional circuit - and difficulties with his serve in particular - caused him falling of the elite rankings and finally splitting with long-term trainer his previous coach.
Currently collaborating with Thomas Johansson and Goetzke, the tennis star has gradually improved in the last few weeks - culminating in a closely contested 7-5 4-6 6-3 victory over opponent Moutet.
It is his first trophy since the Italian tournament and initial on a hardcourt after spring of the previous year.
The win also means the Russian has secured 21 victories at 21 various competitions.
"It's the first time I'm at a event with my children simultaneously, so to secure a title is especially meaningful," said tennis professional Medvedev.
"This title is in tribute of my younger daughter my daughter, because the initial championship I got when my first daughter my daughter was born was for her."
The tennis star, the 2021 US Open champion, had lost his past six championship matches, comprising in Halle previously this season.
His retrieving approach and recurring outbursts on court had led commentators to question if his ability to perform at the elite level was over.
Yet the 29-year-old has implemented adjustments in the last few weeks, attempting to approach the net and play positively, backed up by an improved service.
The champion fought back from a disadvantage in the initial set against the challenging Moutet, securing four of the concluding five exchanges to take the lead.
The pair swapped breaks in the following set before the challenger, striving for his initial professional victory, seized the initiative to force a final set.
The opponent defended four early break points in a tight third set before Medvedev broke to 15 to serve for the match.
Suitably, Medvedev secured the title with a point at the front of the court, with his opponent failing to manage a shot after two hours and 38 minutes.
