Nineteen of Medvedev's twenty-one victories have been earned on hard courts
A comeback the Russian player claimed his first trophy for over two years with a win over Frenchman Moutet in the competition final.
The Russian, a former world number one, has endured a difficult period, managing just one win at the big events and undergoing a difficult moment at the American major.
His unpredictability on the professional circuit - and issues with his service game in specific - caused him dropping out of the world's top 10 and finally parting ways with long-time trainer Cervara.
Presently training with his coach and Rohan Goetzke, the tennis star has steadily progressed in the last few weeks - culminating in a tightly fought competitive victory over Frenchman Moutet.
It is the player's maiden title after the Italian tournament and initial on a hard court since that period of 2023.
Victory also indicates Medvedev has secured twenty-one victories at twenty-one various events.
"This marks the first occasion I have attended a event with my children simultaneously, so to get a trophy is especially meaningful," stated world number 14 the champion.
"This championship is in dedication of my younger daughter my daughter, because the maiden victory I achieved when my first daughter my daughter was born was for her."
The tennis star, the past champion, had been defeated in his previous six championship matches, featuring in Halle previously this season.
His defensive approach and frequent reactions on the playing surface had led commentators to question if his capacity to play at the top level was over.
However the athlete has implemented adjustments in recent weeks, attempting to approach the net and perform positively, reinforced by an better serving game.
Medvedev fought back from a break down in the first set against the tricky Moutet, securing four of the last five games to go ahead.
The competitors exchanged breaks in the following set before the Frenchman, attempting for his maiden professional championship, gained dominance to force a final set.
He defended four initial chances in a tight third set before the Russian won the break to that score to secure the win.
Fittingly, Medvedev secured the title with a shot at the front of the court, with his opponent failing to manage a return after a lengthy match.