Stuttgart looked like they were heading for victory at half-time as they led through a Christian Gentner goal and a Vedad Ibisevic penalty.
Mirko Slomka's men turned things around in the second 45 minutes, though, with Artur Sobiech bringing them back into the game before Jan Schlaudraff levelled from the spot.
Two goals in five minutes from Mohammed Abdellaoue, one coming from the penalty spot, then sealed the win for the Reds over their Europa League rivals.
It was a battle between two of Germany's Europa League participants, both of whom had celebrated wins on Thursday with Hannover qualifying for the knockout stage and Stuttgart boosting their own hopes of following them there.
So confidence was high, and this led to an open game between two sides who belong in the top eight of the Bundesliga.
Stuttgart drew first blood when Gentner provided a cool finish after Ibisevic had missed his acrobatic attempt to turn Raphael Holzhauser's cross in.
Ibisevic was presented with an easier chance to score in the 37th minute after a strangely off-colour Szabolcs Huszti fouled Gentner inside the penalty area, the Bosnian striking his spot-kick into the top corner.
Ibisevic sent a header over the crossbar before Georg Niedermeier was denied by Ron Robert Zieler as Stuttgart threatened to run away with things before the interval.
Schlaudraff was brought on for Huszti at the start of the second half and it was immediately clear that the visitors meant business.
They reduced the arrears in the 57th minute when Lars Stindl sent in a cross from the right and Sven Ulreich spilled the ball to Sobiech, who accepted the gift from close range.
The second penalty of the evening was awarded in the 65th minute for a handball against Serdar Tasci.
Schlaudraff stepped up to choose the opposite corner to Ibisevic and bring the Reds level.
Abdellaoue then entered the game for Sobiech, and within two minutes, he put Hannover in front after Mame Diouf's shot was parried to his feet by Ulreich.
The third penalty of the evening signalled the end for Stuttgart when Arthur Boka downed Stindl inside the box and Abdellaoue scored his second goal in just five minutes on the field to seal victory.