Gian-Luca Waldschmidt's first international goal nine minutes from time looked to have clinched victory for Germany in Wednesday's friendly.
Waldschmidt's strike came after Efecan Karaca had dragged Turkey level for a second time, despite a fairly blatant foul on Florian Neuhaus – who scored on his Germany debut – in the build-up.
Julian Draxler put Germany ahead before Ozan Tufan's stunning finish restored parity in a topsy-turvy encounter, but it ultimately fell to Karaman, who also hit the bar, to have the final say.
Draxler tapped in at the end of a move he started inside six minutes, only for the offside flag to cut Germany's celebrations short.
Germany's captain in the absence of Manuel Neuer had his goal on the stroke of half-time, however, as he raced through to lift a cute finish over Fehmi Mert Gunok.
Julian Brandt might have doubled Germany's tally after the break but for Okay Yokuslu's intervention, before Turkey made it count when Tufan curled a sublime finish over Bernd Leno.
Yet Germany swiftly struck back, debutant Neuhaus combining brilliantly with Kai Havertz – who also assisted the opener – before slotting home.
Neuhaus was involved again nine minutes later, though this time for a Turkey goal. Karaca barged the midfielder over before curling beyond Leno, yet a foul was not given.
Germany thought they had a winner regardless when Gunok failed to keep out Waldschmidt's thumping strike, but Turkey rallied once more.
Substitute Karaman proved to be their hero and, moments after hitting the bar, he cushioned a finish past Leno from Abdulkadir Omur's knock-down.
What does it mean? 2020 just not Germany's year
It has been an infuriating year so far for Germany. With their planned matches in March cancelled due to coronavirus and Euro 2020 postponed, the 2014 World Cup winners drew both of their Nations League matches in September. Ahead of next year's rescheduled Euros, it feels like Low might be reaching a natural end to his time in charge.
Karaman's cameo saves the day for Turkey
Turkey's back-up striker came on in the 63rd minute and managed two shots – one hitting the bar while the other secured a draw – from a total of 20 touches.
Leno leaves a lot to be desired
It would be a stretch to blame the Germany goalkeeper for Turkey's goals, but he made just three saves from six shots on target. While his defence did him no favours, Leno did not stake a claim to challenge Neuer or Marc-Andre ter Stegen.
Ukraine, who were thrashed 7-1 by France on Wednesday, are next up for Germany in the Nations League on Saturday, with Low's team still in search of their first win in the competition. Turkey, meanwhile, go up against Russia on Sunday.