Moritz Leitner gave the visitors the lead in the 12th minute, but Stefan Kiessling and Eren Derdiyok turned the game on its head to move Leverkusen four points clear of Borussia Dortmund.
Stuttgart fell to their third defeat in a week to remain too close to the relegation zone for their liking.
It looked like it could be a different story for the Swabians, however, as they took the lead, like they had in their midweek 2-1 loss to Bayern, with Leitner on target.
His first volleyed attempt was blocked, so he went for a more composed finish, curling the ball into the top left-hand corner from 20 yards out.
Gotoku Sakai nearly undid all of the good work by scoring an own goal at the other end, but his attempted clearance at full stretch just missed a post on its way behind for a corner.
Leverkusen regrouped after falling behind, though, and it was only a matter of time before they did draw level.
Kiessling obliged in the 26th minute when he got a fortunate break to find a gap in the Stuttgart defence and he coolly picked his spot in the far corner of Sven Ulreich's goal.
The hosts continued to push forwards and Son Heung-min saw his shot cannon back off the crossbar, but they nearly fell behind again when Vedad Ibisevic's header was pushed behind by Bernd Leno low down at his right-hand post.
Sidney Sam was sent on for the second half, making his return from a long injury absence to reinforce the Leverkusen attack.
He found himself in the firing line from Stuttgart fans, however, with the game interrupted for a short while before he was able to take a corner from in front of the visiting fans, who pelted the Leverkusen player with objects.
Sam provided the most effective answer possible, though, sending in a cross which Kiessling dummied for Derdiyok to meet with a diving header at the far post.
Stuttgart had chances to level with Ibisevic and substitute Cacau both going close, but Leverkusen held on to bounce back from defeat to Freiburg last weekend and notch their first win of 2014.