Beaten by the Spaniards 32-29 in the preliminary group stage, Germany turned the tables with a masterclass performance despite missing several key players through injury.
They never looked back after racing into a 7-2 lead midway through the first half, with goalkeeper Andreas Wolff in stunning form while right back Kai Haefner was prolific with seven goals at the other end.
The Germans will join hosts Brazil, world champions France, Argentina, Qatar and Egypt at the Aug 5-21 Games in Rio de Janeiro.
Spain will enter one of three additional qualifying tournaments in April, with the top two from each event clinching the remaining six Olympic berths.
Earlier on Sunday, Croatia won the bronze medal with a 31-24 win over Norway.
(Writing by Zoran Milosavljevic in Belgrade; Editing by Toby Davis)
