19 of Medvedev's 21 victories have been achieved on hard courts
A comeback the Russian player claimed his maiden trophy for nearly 30 months with success over Frenchman Moutet in the tournament final.
The athlete, a former number one, has endured a challenging season, winning just one match at the Grand Slams and undergoing a setback at the US Open.
The player's varied form on the ATP Tour - and difficulties with his service game in specific - resulted in him dropping out of the top ten and eventually separating with long-time trainer his previous coach.
Currently working with Thomas Johansson and Goetzke, Medvedev has consistently improved in the past month - peaking in a closely contested competitive victory over challenger Moutet.
This represents the player's first title after the 2023 Rome Masters and first on a hard court after March of that year.
Success also indicates he has achieved twenty-one titles at 21 distinct events.
"For the first time I have attended a tournament with my both daughters at once, so to win a championship is really nice," said tennis professional Medvedev.
"This championship is in tribute of my second daughter my daughter, because the first title I got when my older daughter her name was delivered was for her."
The tennis star, the 2021 US Open champion, had failed in his last six finals, comprising in Halle earlier this year.
His counter-punching strategy and regular reactions on the tennis court had prompted commentators to wonder if his ability to play at the elite level was finished.
But the athlete has made changes in the last few weeks, making an effort to come to the net and perform assertively, backed up by an enhanced serving game.
The champion fought back from a disadvantage in the opening set against the tricky Moutet, securing 4 of the last five points to gain the advantage.
Both players traded service breaks in the second set before Moutet, bidding for his initial tour victory, gained dominance to push for a final set.
He rescued 4 early-game break points in a competitive final set before the champion won the break to 15 to secure the win.
Suitably, he secured the title with a shot at the net area, with the Frenchman unable to manage a return after a lengthy match.