Nineteen of Medvedev's 21 championships have been won on hardcourt
A resurgent Medvedev claimed his first trophy for 882 days with success over Frenchman Moutet in the Almaty Open title decider.
The Russian, a former top-ranked player, has had a challenging period, winning just one match at the big events and experiencing a difficult moment at the US Open.
The player's inconsistency on the tennis tour - and difficulties with his service game in specific - caused him falling of the elite rankings and ultimately splitting with former coach his previous coach.
Now collaborating with his coach and Rohan Goetzke, he has steadily progressed in the last few weeks - culminating in a tightly fought three-set win over challenger Corentin Moutet.
It is the player's first championship after the Italian tournament and initial on a hardcourt since spring of the previous year.
The win also indicates the Russian has secured 21 victories at 21 various events.
"For the first time I have attended a competition with my both daughters simultaneously, so to win a trophy is really nice," said ranked player the champion.
"This victory is in tribute of my child her name, because the initial championship I achieved when my child her name was born was for her."
The athlete, the former major winner, had been defeated in his previous six finals, comprising in Halle in the past months.
The player's defensive strategy and regular emotional displays on the tennis court had caused observers to doubt if his ability to compete at the elite level was finished.
However the player has altered his approach in the last few weeks, striving to advance forward and play assertively, reinforced by an enhanced serve.
Medvedev fought back from a disadvantage in the initial set against the challenging Frenchman, taking 4 of the final five exchanges to take the lead.
The pair exchanged service breaks in the following set before the Frenchman, striving for his first tour championship, took control to force a third set.
He rescued four early opportunities in a tight final set before Medvedev broke to 15 to close out the victory.
Appropriately, Medvedev earned the win with a rally at the net area, with the Frenchman incapable to handle a volley after a lengthy match.