Stindl, an 83rd-minute replacement for Emre Can ensured Joachim Low's finished 2017 without tasting a single defeat, their last loss coming at the hands of France in the European Championship semi-finals last year.
That run looked like coming to an end when Alexandre Lacazette netted twice on Tuesday – the Arsenal striker profiting from Anthony Martial's brilliant footwork for his first before Kylian Mbappe created his second.
In between the Arsenal striker's brace Timo Werner levelled for the hosts as he broke the French offside trap to sweep home Mesut Ozil's pass.
But a second goal looked too much for the hosts as the game entered stoppage time, however substitute Stindl had other ideas as he fired low past Steve Mandanda just 10 minutes after coming on.
A Germany side showing six changes from their draw with England took time to settle and that allowed France to have the better of the opening exchanges, although they initially failed to stretch Kevin Trapp.
Mbappe may well have done when he found space in the 12th minute, but Mats Hummels came to Germany's rescue with a perfectly executed sliding tackle.
Lacazette – preferred in attack to Antoine Griezmann – eventually tested Trapp just before the half-hour mark, while at the other end an important block from Raphael Varane denied Ozil.
Minutes later Trapp had to be alert again to keep Mbappe out low to his right, the Paris-Saint Germain goalkeeper denying his club-mate after a neat Cruyff turn in the penalty area.
Finally, in the 33rd minute, the goal France's pressure deserved came, Martial dancing past Niklas Sule before touching the ball wide of Trapp for Lacazette to apply a simple finish.
Half-time substitute Antonio Rudiger should have brought Germany level seven minutes after his introduction, but the Chelsea defender skewed his effort wide after great work down the left from Julian Draxler.
Germany did not have to wait long for their equaliser as Ozil led a swift counter-attack, his pinpoint throughball releasing Werner and the RB Leipzig forward calmly slotted under Mandanda.
Almost immediately Martial thought he had restored France's lead, but Trapp got down brilliantly to push away his dipping strike.
A Kroos free-kick rattled Mandanda's bar with 20 minutes to play but while the Real Madrid midfielder was wondering how it stayed out, France scored.
Rudiger inexplicably left Lacazette in acres of space 20 yards from goal and the 26-year-old beat Trapp again after being found by Mbappe's pass.
Low introduced Mario Gotze for his first international appearance in just shy of a year and he came good with a superb assist for Stindl, who kept their run going by sliding home a neat 93rd-minute finish.