Nineteen of the Russian's twenty-one victories have been achieved on hardcourt
A resurgent the Russian player secured his first title for nearly 30 months with victory over Frenchman Moutet in the Almaty Open championship match.
Medvedev, a ex- world number one, has had a torrid year, winning just one match at the major tournaments and undergoing a meltdown at the US Open.
His varied form on the professional circuit - and struggles with his serving in particular - resulted in him dropping out of the elite rankings and finally separating with former coach his previous coach.
Currently training with Thomas Johansson and Goetzke, Medvedev has gradually improved in the recent weeks - culminating in a hard-fought 7-5 4-6 6-3 victory over challenger Corentin Moutet.
This represents Medvedev's maiden trophy since the Rome competition and first on a hardcourt from that period of 2023.
Victory also means the Russian has won twenty-one victories at 21 distinct events.
"For the first time I have attended a event with my two daughters together, so to get a title is particularly special," commented tennis professional the champion.
"This championship is in honour of my younger daughter her name, because the initial championship I achieved when my child Alisa was born was for her."
Medvedev, the former major winner, had failed in his past six title deciders, featuring in the German tournament earlier this year.
Medvedev's defensive play style and recurring emotional displays on the playing surface had led some to question if his ability to play at the highest level was over.
But the player has made changes in the last few weeks, striving to approach the net and compete aggressively, reinforced by an improved service.
The champion came back from a deficit in the initial set against the challenging Frenchman, winning four of the concluding five points to gain the advantage.
The competitors swapped service breaks in the middle set before Moutet, striving for his first tour championship, took control to create a final set.
He defended four initial opportunities in a tight third set before Medvedev secured a break to 15 to secure the win.
Appropriately, the winner secured victory with a shot at the net, with his opponent incapable to manage a return after a lengthy match.