Sami Hyypia's men ended a run of six league games without a win against Augsburg on Wednesday, but found themselves immediately under pressure as Martin Laing had an early goal disallowed.
Leverkusen were able to stem the tide until the break, but there was nothing they could do to stop Ken Reichel's thunderous volley opening the scoring early in the second half.
Braunschweig were unable to hold onto the lead for long, however, as Stefan Kiessling earned his side a point from the penalty spot after Marcel Correia handballed inside the penalty area.
Wolfsburg took full advantage of Leverkusen's slip as they moved to within a point after also coming from behind to beat Eintracht Frankfurt 2-1.
Stefan Aigner gave Frankfurt the lead after only 11 minutes and the visitors held on for 58 minutes until Ivica Olic brought the scores level.
With time running out, the game looked to be heading for a draw only for Naldo to produce a sensational long-range strike that flew into the top corner and earned Wolfsburg all three points.
Mainz moved into the final European spot with a comfortable 3-0 victory over Augsburg thanks to goals from Niko Bungert, Johannes Geis and a Marwin Hitz an own goal.
The unfortunate Hitz made a superb save to keep Mainz at bay only for Matthias Ostrzolek to fire a clearance into the keeper's face, and the ball ricocheted into the net.
Bayern Munich followed up retaining their title in midweek by failing to win for only the third time domestically this season as Hoffenheim continued their rollercoaster season with a 3-3 draw.
Anthony Modeste gave Hoffenheim, the league's second-highest scorers behind Bayern, a surprise early lead only for Xherdan Shaqiri and a Claudio Pizarro double to expose their fragile defence, the Bundesliga's leakiest.
Sejad Salihovic pulled a goal back in the closing minute of the first half with a perfectly-placed free kick, and Roberto Firmino sealed a point with a 75th minute equaliser.
Borussia Dortmund moved back into second place in the table as a Marco Reus hat-trick saw them come from two goals down to beat Stuttgart 3-2.
Christian Gentner and Martin Harnik gave Stuttgart an deserved lead, but after Reus had pulled one goal back the dismissal of Georg Niedermeier turned the game in Dortmund's favour.
The defender's second yellow card came after hauling down Robert Lewandowski in the penalty area, Reus converted the spot kick and with the extra man Dortmund were able to find the winning goal with seven minutes to play.
Two sides just outside the bottom three, Freiburg and Nuremberg, met in a vital match at the foot of the table and once again the goals poured in.
Freiburg had to come from behind twice before Felix Klaus secured an important 3-2 victory that moves them five points clear of trouble, and level on points with Werder Bremen and Hannover.
For Nuremberg, it is a fifth league defeat in six and their misery was amplified by the dismissal of Emmanuel Pogatetz in stoppage time for an apparent elbow.