Nineteen of Medvedev's twenty-one championships have been won on hardcourt
A revitalized Medvedev claimed his maiden trophy for 882 days with success over Frenchman Moutet in the Almaty Open title decider.
The athlete, a former number one, has had a challenging year, winning just one match at the major tournaments and suffering a difficult moment at the US Open.
Medvedev's inconsistency on the professional circuit - and struggles with his serving in particular - led to him falling of the world's top 10 and ultimately parting ways with former trainer his previous coach.
Now training with Thomas Johansson and his other coach, Medvedev has gradually progressed in the past month - culminating in a closely contested three-set win over challenger Moutet.
This marks Medvedev's maiden championship after the Italian tournament and first on a hard court after March of the previous year.
Victory also signifies he has achieved twenty-one championships at 21 distinct events.
"This marks the first occasion I am participating in a event with my two daughters together, so to win a trophy is especially meaningful," commented world number 14 Daniil Medvedev.
"This title is in honour of my child Victoria, because the first title I won when my older daughter her name was born was for her."
The tennis star, the 2021 US Open champion, had been defeated in his past six title deciders, including in the German tournament in the past months.
Medvedev's counter-punching approach and recurring emotional displays on the tennis court had prompted commentators to wonder if his capacity to compete at the elite level was finished.
However the 29-year-old has implemented adjustments in the last few weeks, making an effort to approach the net and play aggressively, reinforced by an improved serve.
He fought back from a disadvantage in the first set against the tricky Frenchman, taking 4 of the last five games to take the lead.
The competitors traded breaks in the second set before the challenger, bidding for his maiden professional championship, took control to force a third set.
Moutet rescued 4 initial opportunities in a tight deciding set before Medvedev secured a break to that score to close out the victory.
Suitably, Medvedev secured the title with a shot at the front of the court, with the Frenchman failing to handle a return after over two and a half hours.