Nineteen of Medvedev's 21 titles have been won on hard surfaces
A comeback the Russian player won his initial trophy for over two years with success over Frenchman Moutet in the Almaty Open championship match.
The athlete, a ex- number one, has had a torrid season, winning just one match at the big events and suffering a meltdown at the US Open.
Medvedev's unpredictability on the tennis tour - and issues with his serve in particular - resulted in him dropping out of the top ten and ultimately splitting with former trainer his previous coach.
Presently collaborating with Thomas Johansson and Goetzke, the tennis star has gradually improved in the last few weeks - peaking in a closely contested three-set victory over Frenchman Moutet.
This marks Medvedev's first trophy after the Italian tournament and maiden on a hard surface from that period of that year.
Success also means he has achieved twenty-one titles at twenty-one different competitions.
"This marks the first occasion I am participating in a competition with my children simultaneously, so to secure a championship is especially meaningful," commented world number 14 the champion.
"This title is in honour of my child Victoria, because the first title I won when my older daughter my daughter was born was for her."
The tennis star, the former major winner, had been defeated in his last six championship matches, featuring in the German tournament in the past months.
His retrieving strategy and regular emotional displays on the playing surface had prompted observers to question if his ability to play at the top level was finished.
However the 29-year-old has made changes in recent weeks, making an effort to approach the net and play aggressively, reinforced by an enhanced serving game.
He came back from a disadvantage in the initial set against the tricky Moutet, taking four of the last five exchanges to gain the advantage.
The competitors traded service breaks in the following set before Moutet, bidding for his initial professional victory, seized the initiative to force a decider.
He rescued four initial break points in a tight final set before the Russian broke to 15 to close out the victory.
Fittingly, Medvedev earned victory with a point at the front of the court, with Moutet incapable to control a shot after over two and a half hours.
