19 of Medvedev's twenty-one titles have been won on hard courts
A comeback the Russian player won his initial trophy for nearly 30 months with success over Frenchman Moutet in the competition final.
The Russian, a former world number one, has had a difficult season, achieving just one match at the big events and undergoing a setback at the New York tournament.
Medvedev's varied form on the professional circuit - and difficulties with his serving in especial - led to him dropping out of the elite rankings and eventually splitting with long-time mentor his previous coach.
Presently training with Thomas Johansson and Goetzke, he has gradually improved in the recent weeks - culminating in a hard-fought competitive win over Frenchman Moutet.
It is Medvedev's maiden trophy since the 2023 Rome Masters and initial on a hard court from spring of the previous year.
The win also means he has won 21 victories at twenty-one various tournaments.
"For the first time I have attended a competition with my children together, so to secure a championship is really nice," stated world number 14 the champion.
"This victory is in honour of my younger daughter her name, because the first title I won when my older daughter my daughter was delivered was for her."
The athlete, the 2021 US Open champion, had been defeated in his last six title deciders, including in Halle in the past months.
His retrieving play style and frequent emotional displays on the tennis court had caused some to question if his capacity to play at the highest level was over.
Yet the 29-year-old has implemented adjustments in recent weeks, striving to approach the net and play assertively, supported by an improved service.
The champion fought back from a break down in the first set against the tricky Moutet, securing 4 of the concluding five points to gain the advantage.
The competitors traded breaks in the second set before the challenger, bidding for his initial tour victory, gained dominance to force a third set.
The opponent rescued 4 early opportunities in a close third set before the Russian broke to fifteen to serve for the match.
Suitably, he secured the win with a shot at the front of the court, with the Frenchman incapable to manage a return after over two and a half hours.