Nineteen of Medvedev's 21 titles have been won on hardcourt
A comeback the Russian player won his maiden title for nearly 30 months with a win over Frenchman Moutet in the Almaty Open championship match.
The athlete, a ex- number one, has had a challenging year, achieving just one match at the Grand Slams and undergoing a meltdown at the New York tournament.
Medvedev's unpredictability on the professional circuit - and issues with his serving in especial - led to him dropping out of the elite rankings and finally parting ways with former coach Gilles Cervara.
Currently training with his coach and Goetzke, the tennis star has consistently improved in the past month - culminating in a closely contested three-set win over opponent Moutet.
This represents Medvedev's initial trophy after the Rome competition and maiden on a hard surface since that period of 2023.
The win also indicates Medvedev has achieved twenty-one victories at twenty-one different events.
"It's the first time I'm at a event with my both daughters simultaneously, so to win a championship is really nice," said world number 14 the champion.
"This victory is in tribute of my second daughter Victoria, because the initial championship I got when my first daughter her name was born was for her."
Medvedev, the former major winner, had failed in his last six title deciders, including in Halle in the past months.
Medvedev's defensive play style and frequent emotional displays on the tennis court had prompted commentators to wonder if his skill to play at the elite level was over.
However the player has implemented adjustments in the past month, attempting to advance forward and perform assertively, backed up by an better serve.
The champion recovered from a break down in the first set against the tricky Frenchman, taking four of the concluding five points to gain the advantage.
Both players exchanged service breaks in the following set before Moutet, attempting for his initial tour victory, gained dominance to push for a decider.
Moutet saved four early opportunities in a competitive third set before Medvedev secured a break to 15 to secure the win.
Suitably, he earned the title with a shot at the net, with his opponent unable to handle a shot after a lengthy match.
