Nineteen of Medvedev's 21 victories have been won on hard courts
A comeback Medvedev secured his initial title for 882 days with success over Frenchman Moutet in the tournament title decider.
The Russian, a ex- top-ranked player, has experienced a challenging season, winning just one win at the Grand Slams and experiencing a meltdown at the US Open.
Medvedev's varied form on the tennis tour - and difficulties with his serving in particular - caused him exiting of the elite rankings and eventually parting ways with long-term trainer his previous coach.
Presently collaborating with his coach and Goetzke, Medvedev has consistently progressed in the last few weeks - climaxing in a closely contested 7-5 4-6 6-3 victory over opponent Moutet.
It is his maiden title after the Rome competition and first on a hard court since spring of that year.
Success also indicates the Russian has won twenty-one titles at twenty-one various tournaments.
"For the first time I'm at a competition with my children at once, so to get a title is especially meaningful," commented world number 14 Medvedev.
"This championship is in honour of my second daughter her name, because the first title I won when my first daughter Alisa was born was for her."
Medvedev, the past champion, had lost his previous six title deciders, featuring in Halle earlier this year.
The player's counter-punching strategy and regular emotional displays on court had caused commentators to question if his capacity to perform at the top level was finished.
However the 29-year-old has altered his approach in recent weeks, attempting to come to the net and compete aggressively, backed up by an enhanced serve.
Medvedev came back from a break down in the first set against the tricky Frenchman, winning 4 of the last five points to take the lead.
The pair swapped service breaks in the following set before the challenger, attempting for his first tour championship, took control to push for a final set.
He defended four early chances in a close final set before Medvedev secured a break to that score to close out the victory.
Suitably, Medvedev earned the title with a shot at the net area, with the Frenchman failing to control a volley after over two and a half hours.
