Nineteen of Medvedev's 21 victories have been earned on hard surfaces
A resurgent the Russian player claimed his initial title for 882 days with a win over Frenchman Moutet in the competition championship match.
The athlete, a former world number one, has experienced a torrid year, winning just one win at the major tournaments and suffering a difficult moment at the American major.
His inconsistency on the professional circuit - and struggles with his serving in specific - led to him falling of the top ten and finally splitting with long-term trainer Gilles Cervara.
Now training with Thomas Johansson and Goetzke, the tennis star has consistently advanced in the past month - culminating in a closely contested competitive victory over Frenchman Corentin Moutet.
It is the player's maiden title since the Italian tournament and maiden on a hard surface from that period of the previous year.
Success also means Medvedev has won 21 titles at 21 different tournaments.
"For the first time I am participating in a tournament with my both daughters simultaneously, so to get a title is really nice," said tennis professional the champion.
"This victory is in dedication of my child her name, because the first title I achieved when my child my daughter was delivered was for her."
Medvedev, the former major winner, had lost his last six finals, including in the German tournament in the past months.
His defensive strategy and regular emotional displays on court had caused observers to wonder if his skill to perform at the elite level was finished.
However the player has made changes in the past month, making an effort to approach the net and compete positively, backed up by an better serving game.
The champion fought back from a break down in the first set against the tricky Frenchman, taking 4 of the last five points to go ahead.
The pair swapped breaks in the following set before the Frenchman, striving for his maiden professional championship, seized the initiative to force a final set.
The opponent rescued four early-game break points in a competitive third set before the champion won the break to fifteen to serve for the match.
Suitably, he earned the win with a shot at the net area, with his opponent unable to handle a return after over two and a half hours.
