Joe Enochs' side, who play in Germany's third tier, beat the Bundesliga visitors 3-1 at the Osnatel Arena despite seeing Marcel Appiah sent off after just 15 minutes.
Halil Savran, Marc Heider and Ahmet Arslan went on to secure the victory, with Bobby Wood's penalty counting for little for HSV.
Elsewhere, Liverpool target Naby Keita scored as RB Leipzig romped to a 5-0 victory away to Sportfreunde Dorfmerkingen.
The midfielder netted the final goal after a Marcel Sabitzer double, Timo Werner and Yussuf Poulsen had scored.
Hannover thumped Bonner SC 6-2 away from home, with Martin Harnik and Niclas Fullkrug scoring twice each, while Wolfsburg edged past Eintracht Norderstedt thanks to Ignacio Camacho's solitary goal.