Nico Schulz's last-minute winner stuns Netherlands in the EURO 2020 Qualifiers
Nico Schulz's goal ensured Joachim Low's side gained revenge over their hosts, who had scored two late goals against Germany in November to reach the Nations League finals.
Northern Ireland top Group C after beating Belarus 2-1 at Windsor Park to add to their 2-0 win over Estonia in their opening qualifier.
Koeman's side, who have also played twice, drop to third place following their agonising loss against Germany, who have only played once.
Germany are looking to herald in a new era after a shock group-stage exit at the 2018 World Cup, dispensing with the services of experienced Bayern Munich trio Thomas Muller, Jerome Boateng and Mats Hummels earlier this month.
They were booed off by their own fans after Wednesday's 1-1 friendly draw against Serbia in Wolfsburg and it was looking like being another poor result, but Schulz's goal gave them just their second victory in their past eight competitive games.
Leroy Sane confidently slotted in the opener following Matthijs de Ligt's slip and Serge Gnabry curled in a superb second to put the visitors in the ascendency.
De Ligt's header and Memphis Depay's drilled effort in the second period drew the Dutch level but midfielder Schulz stroked in late on.
Germany were much the better team in the first half, scoring twice including ex-Arsenal winger Gnabry's sublime strike, and Manchester City's Sane and defender Thilo Kehrer saw efforts well saved by Jasper Cillessen.
The Netherlands have struggled in recent years, failing to qualify for Euro 2016 and last summer's World Cup, and have improved since the appointment of ex-Southampton and Everton boss Koeman, but this was a setback.
Fulham winger Ryan Babel should have scored in the opening period but was twice denied by Manuel Neuer and despite getting back into the game, they were unable to hold on.