Nineteen of Medvedev's twenty-one championships have been earned on hard surfaces
A resurgent Medvedev won his initial championship for 882 days with success over Frenchman Moutet in the Almaty Open title decider.
The Russian, a former number one, has had a challenging season, managing just one win at the big events and suffering a difficult moment at the American major.
The player's inconsistency on the tennis tour - and issues with his service game in particular - led to him exiting of the world's top 10 and eventually parting ways with former trainer Gilles Cervara.
Currently training with his coach and Goetzke, the tennis star has steadily progressed in the recent weeks - culminating in a tightly fought three-set victory over challenger Moutet.
This represents Medvedev's initial championship following the Italian tournament and first on a hardcourt from that period of 2023.
Success also signifies he has secured twenty-one championships at 21 distinct events.
"This marks the first occasion I have attended a event with my both daughters together, so to secure a championship is especially meaningful," said world number 14 the champion.
"This title is in dedication of my second daughter my daughter, because the maiden victory I got when my child my daughter was born was for her."
The tennis star, the past champion, had been defeated in his past six title deciders, including in the German tournament earlier this year.
Medvedev's retrieving strategy and frequent reactions on court had led observers to wonder if his ability to play at the top level was over.
Yet the 29-year-old has altered his approach in the past month, attempting to come to the net and compete assertively, reinforced by an better serving game.
Medvedev fought back from a disadvantage in the first set against the tricky opponent, securing four of the last five exchanges to go ahead.
Both players swapped break points in the second set before the Frenchman, striving for his maiden ATP Tour championship, took control to force a third set.
The opponent defended four early-game chances in a tight third set before the champion won the break to that score to close out the victory.
Appropriately, he secured the title with a point at the front of the court, with Moutet unable to manage a shot after over two and a half hours.
