Nineteen of the Russian's 21 titles have been achieved on hard surfaces
A resurgent Medvedev secured his first title for over two years with victory over Frenchman Moutet in the tournament championship match.
The Russian, a ex- world number one, has endured a difficult year, managing just one win at the Grand Slams and experiencing a setback at the New York tournament.
Medvedev's inconsistency on the professional circuit - and struggles with his service game in particular - caused him dropping out of the top ten and ultimately parting ways with long-term coach Cervara.
Now collaborating with Thomas Johansson and Goetzke, he has consistently improved in the last few weeks - climaxing in a closely contested 7-5 4-6 6-3 win over challenger Moutet.
It is Medvedev's initial trophy since the Rome competition and first on a hardcourt after spring of 2023.
Victory also indicates he has won twenty-one championships at 21 different events.
"It's the first time I'm at a tournament with my children simultaneously, so to secure a trophy is particularly special," said ranked player Medvedev.
"This victory is in tribute of my child Victoria, because the initial championship I won when my child her name was born was for her."
Medvedev, the 2021 US Open champion, had lost his last six championship matches, comprising in that event earlier this year.
The player's retrieving strategy and frequent outbursts on the tennis court had prompted commentators to doubt if his ability to compete at the elite level was over.
However the 29-year-old has altered his approach in recent weeks, attempting to advance forward and play positively, supported by an improved serve.
The champion fought back from a deficit in the first set against the tricky Frenchman, winning four of the final five points to go ahead.
The pair swapped break points in the following set before Moutet, striving for his first professional championship, took control to push for a final set.
He defended 4 early break points in a tight deciding set before the champion broke to fifteen to serve for the match.
Suitably, he clinched victory with a shot at the front of the court, with Moutet failing to handle a volley after two hours and 38 minutes.
