19 of Medvedev's 21 championships have been achieved on hard surfaces
A comeback the Russian player won his maiden title for 882 days with victory over Frenchman Moutet in the tournament final.
The athlete, a ex- top-ranked player, has had a torrid period, winning just a single victory at the big events and suffering a setback at the American major.
The player's varied form on the ATP Tour - and struggles with his serve in specific - caused him dropping out of the elite rankings and finally parting ways with long-term coach Gilles Cervara.
Currently working with Thomas Johansson and his other coach, Medvedev has consistently progressed in the recent weeks - peaking in a closely contested 7-5 4-6 6-3 win over Frenchman Moutet.
This represents the player's maiden championship after the Rome competition and first on a hard court after spring of that year.
The win also means Medvedev has won 21 championships at twenty-one various tournaments.
"For the first time I'm at a tournament with my both daughters at once, so to secure a championship is really nice," said world number 14 Medvedev.
"This title is in dedication of my child her name, because the initial championship I achieved when my first daughter her name was delivered was for her."
The athlete, the past champion, had been defeated in his past six title deciders, comprising in the German tournament previously this season.
The player's retrieving strategy and regular reactions on the tennis court had led commentators to wonder if his ability to perform at the top level was concluded.
Yet the athlete has made changes in the last few weeks, making an effort to approach the net and perform aggressively, supported by an better serve.
The champion recovered from a disadvantage in the initial set against the difficult opponent, securing 4 of the concluding five points to take the lead.
Both players swapped break points in the following set before the Frenchman, striving for his initial ATP Tour title, took control to force a decider.
The opponent rescued four initial chances in a close deciding set before Medvedev secured a break to fifteen to serve for the match.
Appropriately, he secured victory with a shot at the net, with his opponent failing to handle a shot after two hours and 38 minutes.
