The 28-year-old Monaco, ranked 14th in the world and seeded third here, added to his titles from Vina del Mar in Chile and Houston, Texas on clay this year to bring his career tally to six.
Former world number two Haas, 34, was playing his second final of the season, after beating Wimbledon champion Roger Federer on grass to lift the Halle title last month.
"He played some fantastic tennis but I am happy and proud to have played another final here on home soil in front of my family," said Haas, who has mounted a resurgence in the world rankings this year after falling outside the top 200 following hip and shoulder injuries.
"That gives me motivation for the future."
It was his fourth consecutive defeat at the hands of Monaco, who will break into the world top ten when the latest rankings are announced on Monday.
Juan Monaco wins Hamburg title
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