19 of the Russian's 21 titles have been won on hard surfaces
A comeback Medvedev claimed his initial trophy for nearly 30 months with victory over Frenchman Moutet in the competition title decider.
The Russian, a former number one, has endured a torrid period, achieving just one win at the big events and suffering a difficult moment at the US Open.
The player's unpredictability on the ATP Tour - and difficulties with his serve in especial - led to him dropping out of the elite rankings and eventually separating with long-time trainer Gilles Cervara.
Presently working with Thomas Johansson and Rohan Goetzke, the tennis star has consistently advanced in the last few weeks - climaxing in a closely contested three-set win over opponent Moutet.
This represents the player's maiden title after the Rome competition and initial on a hardcourt since March of the previous year.
Victory also signifies the Russian has secured 21 victories at 21 distinct events.
"This marks the first occasion I am participating in a tournament with my both daughters at once, so to win a trophy is particularly special," commented tennis professional the champion.
"This title is in dedication of my child her name, because the maiden victory I won when my older daughter my daughter was born was for her."
The athlete, the former major winner, had failed in his previous six title deciders, featuring in the German tournament earlier this year.
His defensive approach and recurring outbursts on court had led observers to wonder if his skill to perform at the elite level was finished.
However the 29-year-old has made changes in the past month, striving to approach the net and perform assertively, reinforced by an better serving game.
Medvedev recovered from a disadvantage in the first set against the difficult Moutet, taking four of the final five points to gain the advantage.
The competitors traded service breaks in the following set before the challenger, striving for his initial ATP Tour victory, gained dominance to force a third set.
The opponent defended four early-game chances in a tight final set before the Russian won the break to fifteen to secure the win.
Fittingly, the winner clinched victory with a shot at the front of the court, with his opponent unable to manage a return after a lengthy match.
