Nineteen of Medvedev's 21 titles have been achieved on hard surfaces
A resurgent the Russian player claimed his maiden championship for nearly 30 months with a win over Frenchman Moutet in the tournament final.
The athlete, a ex- world number one, has had a difficult period, achieving just one match at the major tournaments and suffering a setback at the New York tournament.
His unpredictability on the tennis tour - and issues with his serving in especial - led to him exiting of the top ten and eventually parting ways with long-term trainer his previous coach.
Now training with Thomas Johansson and Goetzke, he has consistently progressed in the last few weeks - culminating in a tightly fought 7-5 4-6 6-3 triumph over challenger Moutet.
It is Medvedev's initial title since the Rome competition and initial on a hard court from that period of the previous year.
The win also means he has won twenty-one victories at 21 different events.
"For the first time I am participating in a competition with my children simultaneously, so to get a title is particularly special," said world number 14 the champion.
"This title is in honour of my second daughter Victoria, because the first title I won when my first daughter her name was born was for her."
The athlete, the former major winner, had been defeated in his past six title deciders, comprising in that event previously this season.
His defensive approach and regular outbursts on the playing surface had prompted some to wonder if his ability to compete at the top level was finished.
Yet the player has implemented adjustments in the last few weeks, attempting to advance forward and play positively, supported by an improved service.
He recovered from a deficit in the first set against the tricky opponent, taking four of the concluding five points to go ahead.
Both players swapped breaks in the second set before Moutet, attempting for his maiden ATP Tour championship, gained dominance to push for a final set.
Moutet defended four early-game chances in a competitive deciding set before the Russian broke to 15 to serve for the match.
Fittingly, Medvedev clinched the win with a rally at the front of the court, with the Frenchman failing to handle a return after over two and a half hours.
