Nineteen of Medvedev's 21 titles have been earned on hard courts
A comeback the Russian player won his initial trophy for over two years with victory over Frenchman Moutet in the Almaty Open title decider.
The Russian, a former number one, has endured a difficult season, managing just one win at the big events and suffering a meltdown at the US Open.
The player's unpredictability on the professional circuit - and struggles with his serve in specific - resulted in him exiting of the world's top 10 and finally separating with long-time coach Gilles Cervara.
Presently working with Thomas Johansson and Goetzke, the tennis star has steadily advanced in the last few weeks - culminating in a closely contested 7-5 4-6 6-3 triumph over opponent Corentin Moutet.
This marks the player's initial title after the 2023 Rome Masters and initial on a hardcourt since spring of 2023.
Victory also means he has secured 21 championships at 21 various competitions.
"For the first time I am participating in a event with my two daughters together, so to win a title is particularly special," said world number 14 Medvedev.
"This title is in dedication of my second daughter Victoria, because the maiden victory I achieved when my child her name was born was for her."
The athlete, the 2021 US Open champion, had lost his past six title deciders, featuring in the German tournament earlier this year.
The player's counter-punching approach and frequent reactions on the playing surface had prompted commentators to question if his ability to compete at the top level was concluded.
Yet the 29-year-old has made changes in the last few weeks, making an effort to approach the net and perform aggressively, supported by an improved serving game.
Medvedev recovered from a deficit in the first set against the challenging Moutet, winning four of the concluding five points to go ahead.
The pair swapped break points in the second set before the Frenchman, attempting for his initial tour title, seized the initiative to create a final set.
Moutet rescued 4 early break points in a tight final set before Medvedev secured a break to that score to close out the victory.
Fittingly, Medvedev earned victory with a rally at the net area, with his opponent failing to handle a shot after two hours and 38 minutes.
