Nineteen of the Russian's 21 championships have been earned on hard surfaces
A comeback Medvedev claimed his first championship for nearly 30 months with victory over Frenchman Moutet in the tournament final.
The athlete, a former world number one, has had a challenging season, winning just one match at the Grand Slams and suffering a setback at the New York tournament.
His varied form on the professional circuit - and difficulties with his service game in particular - resulted in him exiting of the top ten and finally separating with long-time trainer his previous coach.
Now training with Thomas Johansson and his other coach, Medvedev has steadily progressed in the last few weeks - culminating in a tightly fought competitive triumph over opponent Moutet.
It is Medvedev's maiden championship since the Italian tournament and maiden on a hard court since spring of the previous year.
Victory also means Medvedev has secured twenty-one titles at 21 different events.
"This marks the first occasion I have attended a event with my two daughters together, so to get a trophy is especially meaningful," said world number 14 the champion.
"This title is in honour of my second daughter her name, because the initial championship I got when my child my daughter was delivered was for her."
Medvedev, the 2021 US Open champion, had failed in his past six title deciders, comprising in that event earlier this year.
The player's retrieving strategy and regular reactions on the playing surface had led some to wonder if his capacity to perform at the top level was finished.
However the athlete has altered his approach in the past month, striving to advance forward and compete aggressively, reinforced by an improved service.
He fought back from a disadvantage in the initial set against the tricky opponent, winning 4 of the final five games to take the lead.
Both players traded break points in the middle set before Moutet, bidding for his initial ATP Tour victory, gained dominance to force a final set.
The opponent rescued four early break points in a tight final set before Medvedev broke to fifteen to close out the victory.
Fittingly, he earned the title with a point at the net area, with his opponent failing to manage a shot after two hours and 38 minutes.
