Nineteen of Medvedev's 21 victories have been earned on hardcourt
A comeback the Russian player secured his initial trophy for nearly 30 months with success over Frenchman Moutet in the competition championship match.
The Russian, a ex- number one, has endured a torrid period, achieving just one match at the Grand Slams and suffering a setback at the US Open.
His varied form on the ATP Tour - and difficulties with his serving in especial - caused him dropping out of the elite rankings and finally parting ways with long-term trainer Cervara.
Currently training with his coach and Rohan Goetzke, he has steadily improved in the last few weeks - climaxing in a tightly fought three-set victory over opponent Moutet.
This represents Medvedev's first trophy since the Rome competition and initial on a hard court since March of 2023.
Success also indicates the Russian has achieved 21 championships at twenty-one distinct events.
"This marks the first occasion I'm at a event with my both daughters together, so to get a trophy is really nice," said world number 14 the champion.
"This championship is in honour of my second daughter Victoria, because the initial championship I won when my first daughter Alisa was born was for her."
The tennis star, the former major winner, had been defeated in his last six finals, including in Halle previously this season.
His counter-punching approach and recurring reactions on court had caused some to wonder if his skill to perform at the highest level was concluded.
But the player has altered his approach in the last few weeks, attempting to advance forward and perform assertively, backed up by an better serving game.
Medvedev came back from a break down in the first set against the difficult Moutet, winning 4 of the concluding five points to gain the advantage.
Both players exchanged break points in the middle set before the Frenchman, attempting for his initial professional victory, took control to force a third set.
The opponent defended four early break points in a competitive final set before the Russian broke to 15 to secure the win.
Fittingly, Medvedev earned victory with a shot at the front of the court, with the Frenchman incapable to control a return after over two and a half hours.
