The 23-year-old Kohlschreiber, in his first-ever ATP final, gained an early break of serve in the second set and had the only break of the third in the fifth game.
He went on to hold serve, claiming victory on his third match point to capture the first prize of $75,000.
"It's such an amazing thing to win your first ATP title and to do it in Germany," said Kohlschreiber. "I'm so happy. This is just a crazy day and I need a few days before this sinks in."
The third-seeded Youzhny, playing in his third ATP final of 2007, fell to 1-2 in title matches this season.
Celebrity Families of 2014 [PHOTOS]