Nineteen of the Russian's twenty-one victories have been achieved on hardcourt
A resurgent Medvedev secured his initial championship for nearly 30 months with a win over opponent Moutet in the competition final.
The Russian, a former number one, has endured a difficult year, managing just one win at the big events and suffering a setback at the American major.
The player's inconsistency on the ATP Tour - and difficulties with his service game in especial - led to him exiting of the top ten and eventually parting ways with long-term trainer his previous coach.
Currently training with Thomas Johansson and Goetzke, he has gradually improved in the past month - peaking in a hard-fought 7-5 4-6 6-3 victory over opponent Moutet.
This marks the player's first title following the 2023 Rome Masters and maiden on a hard court since spring of the previous year.
Success also signifies the Russian has achieved 21 championships at twenty-one distinct competitions.
"For the first time I am participating in a competition with my two daughters together, so to secure a title is especially meaningful," stated world number 14 Medvedev.
"This victory is in honour of my child Victoria, because the first title I achieved when my child her name was delivered was for her."
Medvedev, the past champion, had been defeated in his past six finals, comprising in Halle in the past months.
The player's defensive play style and regular reactions on the playing surface had prompted commentators to wonder if his capacity to compete at the top level was finished.
However the 29-year-old has altered his approach in the last few weeks, attempting to advance forward and perform positively, backed up by an better serving game.
Medvedev came back from a break down in the first set against the difficult opponent, securing four of the final five points to take the lead.
Both players exchanged breaks in the middle set before the challenger, attempting for his maiden ATP Tour title, seized the initiative to force a third set.
He rescued four initial chances in a close deciding set before the Russian broke to that score to close out the victory.
Suitably, Medvedev clinched victory with a shot at the net area, with his opponent incapable to handle a shot after two hours and 38 minutes.