19 of Medvedev's 21 championships have been earned on hard courts
A resurgent the Russian player won his initial trophy for over two years with a win over Frenchman Moutet in the tournament championship match.
The athlete, a former top-ranked player, has experienced a difficult season, achieving just a single victory at the major tournaments and undergoing a meltdown at the American major.
The player's varied form on the tennis tour - and issues with his service game in specific - caused him exiting of the elite rankings and finally parting ways with long-term coach Cervara.
Now working with his coach and Goetzke, Medvedev has gradually advanced in the last few weeks - peaking in a closely contested three-set victory over Frenchman Moutet.
This represents his maiden trophy after the Italian tournament and first on a hard surface after spring of the previous year.
Victory also indicates he has secured 21 titles at twenty-one different events.
"For the first time I'm at a tournament with my children at once, so to win a title is particularly special," said ranked player Medvedev.
"This title is in tribute of my second daughter Victoria, because the maiden victory I got when my child Alisa was delivered was for her."
Medvedev, the former major winner, had failed in his previous six title deciders, comprising in Halle previously this season.
Medvedev's defensive strategy and frequent reactions on court had prompted commentators to question if his ability to play at the top level was over.
However the athlete has altered his approach in the last few weeks, making an effort to approach the net and play positively, reinforced by an improved serving game.
Medvedev fought back from a disadvantage in the initial set against the difficult Moutet, winning four of the final five games to gain the advantage.
The competitors traded breaks in the second set before the challenger, bidding for his initial ATP Tour victory, took control to create a decider.
Moutet defended 4 early chances in a competitive final set before Medvedev broke to fifteen to serve for the match.
Appropriately, Medvedev earned the title with a point at the net, with Moutet unable to handle a shot after over two and a half hours.