19 of the Russian's 21 titles have been achieved on hardcourt
A comeback Medvedev claimed his first trophy for nearly 30 months with a win over Frenchman Moutet in the tournament title decider.
Medvedev, a ex- world number one, has endured a torrid year, achieving just one match at the big events and undergoing a setback at the New York tournament.
His inconsistency on the professional circuit - and difficulties with his serve in specific - led to him exiting of the top ten and eventually separating with long-time coach Gilles Cervara.
Presently working with Johansson and Goetzke, he has steadily improved in the past month - peaking in a hard-fought competitive victory over challenger Moutet.
It is the player's first championship after the Rome competition and first on a hard surface from that period of the previous year.
The win also signifies Medvedev has secured twenty-one victories at 21 different events.
"It's the first time I'm at a event with my children at once, so to get a title is really nice," stated ranked player the champion.
"This championship is in tribute of my child her name, because the initial championship I achieved when my older daughter Alisa was born was for her."
Medvedev, the former major winner, had failed in his previous six title deciders, featuring in Halle earlier this year.
His counter-punching play style and recurring reactions on the tennis court had prompted observers to wonder if his ability to perform at the elite level was concluded.
Yet the athlete has made changes in recent weeks, striving to approach the net and compete assertively, backed up by an better service.
Medvedev recovered from a disadvantage in the initial set against the challenging Moutet, taking four of the last five games to take the lead.
The competitors swapped service breaks in the second set before Moutet, bidding for his initial tour victory, seized the initiative to push for a final set.
He saved four early-game chances in a tight deciding set before the Russian secured a break to that score to secure the win.
Fittingly, the winner clinched the title with a rally at the net, with his opponent incapable to control a return after two hours and 38 minutes.
