Nineteen of Medvedev's 21 titles have been earned on hardcourt
A resurgent the Russian player won his initial title for over two years with a win over Frenchman Moutet in the Almaty Open title decider.
The Russian, a former world number one, has endured a difficult period, winning just a single victory at the Grand Slams and undergoing a difficult moment at the American major.
Medvedev's unpredictability on the tennis tour - and difficulties with his serving in specific - led to him exiting of the top ten and finally splitting with former mentor his previous coach.
Currently training with Thomas Johansson and Goetzke, he has consistently progressed in the past month - climaxing in a hard-fought competitive triumph over challenger Moutet.
This represents his initial championship following the Rome competition and maiden on a hard court since that period of the previous year.
Success also indicates Medvedev has achieved twenty-one titles at 21 distinct events.
"For the first time I have attended a competition with my both daughters at once, so to secure a title is really nice," commented world number 14 Daniil Medvedev.
"This championship is in honour of my younger daughter her name, because the first title I got when my first daughter her name was born was for her."
The tennis star, the former major winner, had failed in his previous six title deciders, including in the German tournament previously this season.
Medvedev's defensive play style and frequent reactions on the tennis court had caused observers to wonder if his skill to compete at the top level was over.
But the athlete has implemented adjustments in the last few weeks, attempting to approach the net and perform aggressively, backed up by an better serving game.
Medvedev fought back from a deficit in the opening set against the difficult Moutet, taking 4 of the concluding five games to take the lead.
Both players swapped service breaks in the second set before Moutet, attempting for his initial professional victory, seized the initiative to create a final set.
Moutet rescued four early break points in a tight deciding set before Medvedev secured a break to fifteen to secure the win.
Suitably, the winner clinched the title with a rally at the front of the court, with Moutet failing to manage a return after two hours and 38 minutes.