The win gave the Dutch their third gold medal and 10th medal overall in hockey since 1928. They last won gold at the Sydney Games in 2000, having lost in the 2004 and 2012 finals.
German Chancellor Olaf Scholz was in the stands to watch his country as cries of 'Holland!' and 'Deutschland!' competed with each other throughout a tightly contested defensive match-up.
Germany and the Netherlands were held to six and seven shots respectively, with the Germans having 57% possession but the Dutch double the attacking circle penetrations with 20.
Netherlands captain Thierry Brinkman finally opened the scoring in the 46th minute by redirecting a shot from teammate Koen Bijen that was lifted over Danneberg.
"The whole team was amazing the whole tournament. Our culture is so good. I think we can stay with it for the next couple of years," Brinkman told a press conference.
"Our group is forever. We're really happy and we'll party really well this week."
Germany defender Gonzalo Peillat saved his side in the 49th minute by catching a shot in the middle of his stick on the goal line that had gone over a prone Danneberg, who had made a diving save to keep out a shot moments before.
Germany then immediately pressured the Dutch defence which gave up a penalty corner. Midfielder Thies Prinz used it to pull his side level by backing up out of the circle and lining up a shot that flew past goalkeeper Pirmin Blaak.
The Netherlands were awarded a penalty corner in the final minute, which defender Jip Janssen ripped off his stick but it went wide and the game went to a penalty shootout.
Danneberg stifled the first penalty by Jonas de Geus by diving to block the shot, while Pirmin responded by holding the ball between his gloves from Niklas Wellen.
Danneberg also kept the second penalty out, catching it with his pad hand while diving. Pirmin then caught Hannes Mueller's attempt with his pad to keep the shootout score at 0-0.
Brinkman netted the first shootout goal of the set with a spinning backhand lifting the ball between Danneberg's leg and stick. Pirmin then saved Prinz's shot with his pad hand.
Thijs van Dam followed his skipper and slotted the ball between Danneberg's legs, leaving the Germans on the ropes.
Justus Weigand scored the first German shootout goal by working around Pirmin's pad side, but it was too late as Telgenkamp's shot rang off the boards to give the Dutch gold, leaving Germany with their last shot in hand.
Telgenkamp got in Danneberg's face afterwards with a jeer, nearly starting a scrum as Niklas Wellen rushed over to defend his goalkeeper.
