An entertaining first half saw both teams score inside the first five minutes, with Aleix Garcia firing into the near post after Christian Kofane released him following a fast break.
Stuttgart responded immediately, though, as Ermedin Demirovic - who was undoubtedly the hosts’ biggest threat - played a neat one-two with Nikolas Nartey before striking his 15th competitive strike of the season into the far corner.
As well as giving the Swabians an immediate uplift, the goal also marked Demirovic's third successive goalscoring outing.
Given the high stakes surrounding this clash, both sides continued to attack vigorously, and both goalkeepers were called into action in quick succession, with Alexander Nubel saving Ibrahim Maza’s volley later in the first half.
Mark Flekken then parried away Chris Fuhrich’s cross-come-shot, and while the reliable Demirovic was there for the follow-up, his goalbound strike was brilliantly blocked by Edmond Tapsoba.
The striker only continued to terrorise Leverkusen’s defence, though, and won a penalty on the stroke of half-time when Tapsoba tripped him up inside the box. Maximilian Mittelstadt coolly converted the subsequent spot kick to complete the turnaround.
It was a very timely event, and Stuttgart built on that immediately after half-time, scoring an apparent third when an offside Demirovic slotted home after Flekken spilt Deniz Undav's original shot.
The Dutchman was then called into action again, first stopping Angelo Stiller’s effort before palming over Jeff Chabot’s header from a corner.
However, he was helpless to stop Undav poking home Jamie Leweling’s whipped cross for his 19th league goal this term - his best-ever return in the Bundesliga.
Leverkusen looked more threatening in the latter stages but ultimately packed little punch, as they surrendered their advantage in the race for UCL football heading into the final day.
As for Stuttgart, they are in the driving seat for a top-four finish, after recording a league double over their opponents - something of a statement in itself, given that they had won just once in 29 H2Hs (D8, L20) prior to this season.