Nineteen of Medvedev's 21 victories have been achieved on hardcourt
A resurgent Medvedev won his first trophy for 882 days with victory over Frenchman Moutet in the competition final.
Medvedev, a former number one, has had a challenging season, achieving just a single victory at the Grand Slams and suffering a difficult moment at the New York tournament.
His varied form on the ATP Tour - and issues with his serving in especial - caused him falling of the elite rankings and eventually parting ways with long-time coach his previous coach.
Now collaborating with his coach and Goetzke, he has steadily improved in the recent weeks - peaking in a tightly fought competitive victory over opponent Moutet.
This marks Medvedev's first title since the Italian tournament and initial on a hardcourt from that period of the previous year.
The win also indicates Medvedev has achieved twenty-one victories at twenty-one various tournaments.
"This marks the first occasion I'm at a tournament with my children together, so to secure a title is particularly special," said world number 14 the champion.
"This championship is in dedication of my second daughter my daughter, because the maiden victory I achieved when my child her name was born was for her."
Medvedev, the past champion, had lost his past six championship matches, featuring in that event previously this season.
Medvedev's retrieving play style and frequent outbursts on court had caused commentators to question if his ability to compete at the elite level was concluded.
But the athlete has altered his approach in the last few weeks, attempting to approach the net and perform aggressively, supported by an enhanced serve.
Medvedev came back from a deficit in the opening set against the difficult opponent, taking 4 of the last five exchanges to go ahead.
The competitors swapped break points in the second set before the challenger, attempting for his initial tour championship, took control to push for a third set.
Moutet defended 4 early break points in a close third set before the Russian won the break to 15 to secure the win.
Suitably, he clinched the win with a point at the net, with his opponent incapable to control a volley after a lengthy match.