Mario Gomez fired the Bavarians into the lead with a superb solo effort in the 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.
The leaders, who are also favourites to lift the German Cup and are through to the Champions League quarter-finals, set a Bundesliga record by chalking up their 12th away win of the season.
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.
"We clearly dominated in the first half but were made to battle harder in the second," Bayern coach Jupp Heynckes told reporters as his squad stood on the verge of clinching the title quicker than anyone else in the 50-year history of the Bundesliga.
"Overall I am satisfied with my team's performance."
Heynckes made half a dozen changes to the side that edged past Arsenal on Wednesday to reach the Champions League last eight, 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 Bonisch 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 half-time 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.
DORTMUND DEMOLITION
Champions Dortmund, who face Malaga in next month's Champions League quarter-finals, netted three times in four minutes at the end of the first half and Lewandowski set a club record by scoring in his eighth straight league game.
Jonathan Schmid had given eighth-placed Freiburg a 28th-minute lead but Lewandowski levelled 13 minutes later.
Turkey midfielder Sahin made it 2-1 before Poland striker Lewandowski added a third with a brilliant individual goal in stoppage time, his 19th of the season in the league.
Sahin, who returned to Dortmund in the January transfer window after unhappy spells at Real Madrid and Liverpool, grabbed his second goal in the 72nd minute.
Lewandowski then did well to set up the talented Leonardo Bittencourt for his first Bundesliga goal six minutes later.
"It was a deserved victory although I can understand Freiburg are a
