Jakub Kiwior's bouncing header snatched only the second victory for the hosts over the Germans in 90 years. Germany have now won only three of their last 10 international matches.
Four-time world champions Germany, who play Colombia next week in their last international before the summer break, now have less than a year to build a battle-worthy team for their home Euros.
Following their disappointing first round World Cup exit in Qatar last year, they have so far failed to show clear signs of recovery even though their second half performance on Friday was improved from their opening 45 minutes.
They have managed just one win -- over Peru -- in their four matches since the World Cup.
"It is still a long way and there is enough time," said Germany coach Hansi Flick. "I am very confident in relation to the path we have to take."
"We will have a functioning team by next June. It is a process we will go together. The team is ready to do it.
"We are in a phase which is not that easy. We will come out of it. We can build on our second half performance even though the result is, of course, not enough for us."
The Germans, who needed two late goals to rescue a 3-3 draw against Ukraine on Monday, were almost caught out when Jakub Blaszczykowski chased down a deep cross but Malick Thiaw's well-timed tackle denied the 37-year-old at the edge of the box.
The hosts kept breaking through the shaky German backline with Jakub Kaminski's shot from a tight angle saved by keeper Marc-Andre ter Stegen.
He was beaten in the 31st when Kiwior's glancing header bounced off the ground first and then floated past Ter Stegen who got a hand to the ball but could not push it wide.
The Germans looked sharper in the second half and piled on the pressure right after the restart, threatening with Robin Gosens before Joshua Kimmich saw his effort bounce off the crossbar four minutes after the restart.
Thiaw, making his Germany debut, got close to an equaliser with a fine turn and shot in the box but keeper Wojciech Szczesny produced his best moment of the night to block it.
Germany had a string of late chances but could not find an equaliser that would alleviate some of the pressure they and Flick will now face on their return.
"I had hoped we could celebrate a success in order to change the mood and get the country behind us," said Gosens, whose pace on the wing in the second half did Germany well.
"We all know that can only happen with results and wins. We played a good second half but it is time we start getting rewarded for it."
