Mario Gomez fired the Bavarians into the lead with a superb solo effort in 37th minute but Simon Rolfes grabbed the equaliser in the 75th.
Bayern, who will lift the title if they win their next match and second-placed Borussia Dortmund draw, avenged their only league defeat this season when Bastian Schweinsteiger's 87th-minute free kick deflected into the net off Philipp Wollscheid's shoulder.
Dortmund demolished Freiburg 5-1 with two goals apiece from Bundesliga top scorer Robert Lewandowski and playmaker Nuri Sahin to sprint four points clear of third-placed Leverkusen.
Bayern have 69 points with eight games left, Dortmund are on 49 and Leverkusen 45.
Coach Jupp Heynckes made half a dozen changes to the Bayern team that edged past Arsenal on Wednesday to reach the Champions League quarter-finals, with Gomez replacing the club's top scorer Mario Mandzukic.
The Germany forward made the most of a rare start when he picked up a Xherdan Shaqiri cross, left Daniel Carvajal and Sebastian Boenisch trailing in his wake and drilled the ball in from 15 metres for his seventh league goal of the season.
Bayern were the better side for much of the game and went close on the stroke of halftime when a Luiz Gustavo header was cleared off the line by Gonzalo Castro.
Heynckes then took Gomez off and replaced winger Arjen Robben with central defender Daniel van Buyten and Leverkusen got back in the game as Rolfes poked in a corner at the far post.
Bayern, though, hit back with the late own goal earning maximum points.