France were back on level terms just after the hour mark when a well-marked Griezmann was able to redirect a flawless Lucas Hernandez cross over Neuer to make it 1-1.
The Germans deservedly led through a Kroos penalty after a sliding Presnel Kimpembe handled a Sane cross, but Loew's youthful frontline was unable to capitalise on further opportunities.
Antoine Griezmann hit a pair of second-half goals, including the victor from the spot, as France recovered from falling behind to a Toni Kroos penalty to inflict a sixth defeat on Germany in their past 10 matches.
"There is nothing better for my team, my players, than this".
Germany now face the very real prospect of relegation from Group 1 of the UEFA Nations League, unless they see off Holland in Gelsenkirchen next month.
Griezmann, however, made no mistake from the spot.
Germany's confidence has taken a bashing since their group stage exit at the World Cup as defending champions and two unconvincing performances in the Nations League a 0-0 home draw against France and a 3-0 loss away to the Netherlands last Saturday. "If we'd been able to score a second we could have played in a calmer manner and won the match".
"But the penalty was totally unjustified".
"The French did not cope with our setup in the first half", he added. "I've watched it back on the replay". He picked out midfielder Blaise Matuidi's run and centre half Mats Hummels was adjudged to have impeded Matuidi, although there was no video review available to the referee and contact appeared minimal.
Deschamps said: "This team has character, we have proved that already. When you are not having a good day, you can change the system and the players, but (the French team) never gives up, and that's how we keep going". "Tactically speaking, we weren't making enough effort for one another", Griezmann said.
It was a sixth defeat in the past 10 games for Löw's squad, who crashed out of the group stages at the World Cup in Russian Federation and remain bottom of their Nations League table with just one point from three matches.