Nineteen of the Russian's twenty-one titles have been achieved on hardcourt
A resurgent Medvedev secured his initial title for 882 days with victory over Frenchman Moutet in the Almaty Open title decider.
Medvedev, a ex- world number one, has experienced a torrid season, achieving just a single victory at the Grand Slams and undergoing a setback at the US Open.
The player's unpredictability on the tennis tour - and difficulties with his serve in particular - caused him dropping out of the elite rankings and ultimately splitting with long-term coach Gilles Cervara.
Presently collaborating with Thomas Johansson and Goetzke, the tennis star has steadily progressed in the past month - peaking in a tightly fought three-set victory over opponent Moutet.
This represents his first trophy following the Rome competition and initial on a hard court after spring of 2023.
Victory also signifies Medvedev has secured twenty-one championships at 21 different competitions.
"For the first time I'm at a competition with my two daughters simultaneously, so to get a trophy is really nice," commented world number 14 Daniil Medvedev.
"This championship is in dedication of my second daughter Victoria, because the initial championship I won when my older daughter Alisa was born was for her."
The tennis star, the 2021 US Open champion, had failed in his previous six finals, featuring in that event in the past months.
Medvedev's defensive play style and recurring outbursts on court had caused observers to doubt if his skill to perform at the top level was finished.
Yet the player has altered his approach in the last few weeks, striving to approach the net and perform positively, reinforced by an better service.
The champion came back from a deficit in the initial set against the difficult opponent, securing 4 of the last five games to go ahead.
Both players exchanged break points in the middle set before the Frenchman, striving for his first tour victory, seized the initiative to create a decider.
Moutet defended four early break points in a close deciding set before the champion broke to 15 to close out the victory.
Suitably, Medvedev earned the win with a point at the net area, with the Frenchman failing to handle a volley after a lengthy match.