Toni Kroos put the visitors ahead in the 30th minute but Pep Guardiola's men were immediately pegged back by Sidney Sam
Toni Kroos opened the scoring for Bayern in the first half on Saturday before Sidney Sam, scorer of the winner when the sides met in Munich last season, equalised less than 60 seconds later following an error by Manuel Neuer.
That defeat to Leverkusen was the last time Bayern had lost in the league, but they never looked like losing again - dominating their hosts from start to finish - but they were unable to find a winner against a stubborn home rear-guard.
The result took Munich one point clear of Borussia Dortmund at the Bundesliga summit, while Leverkusen remain in third, level on points with Jurgen Klopp's side.
Leverkusen boss Sami Hyypia made three changes to the side that beat Real Sociedad in midweek, including Emre Can against his former club in place of Roberto Hilbert, while Bayern made just one change from Wednesday night's crushing of Manchester City.
And the Bavarians started the match where they left off in Manchester, dominating Leverkusen in the early stages.
Pep Guardiola's side could have been 2-0 up within the first 10 minutes, with first Kroos then Thomas Muller dragging efforts wide of the goal when they really should both have hit the target.
Franck Ribery went close after 18 minutes, outmuscling Lars Bender before drilling a low 20-yard shot just wide of Leno's right post.
For the opening goal Ribery turned provider, skinning Leverkusen centre-back Omer Toprak before pulling back to Kroos, who hammered home a left-footed shot.
The hosts had barely been in the game, but they equalised almost immediately following a mistake by Neuer, who flapped at a cross giving Sebastian Boenisch a chance to score. Neuer saved well but the rebound fell at the feet of Sam, who slotted into an empty net.
Despite the equaliser, Bayern's pressure continued unabated and Muller had a brilliant chance to equalise after Ribery and David Alaba combined well on the left to find the German, but he inexplicably headed wide with an open goal gaping as the sides went in at the break level.
The second half began with a penalty shout for Bayern turned down by the referee, who had failed to spot the blatant shirt pull by Toprak on Muller.
Ribery then had efforts saved by Leno in as many minutes, the first a blistering left-footed volley, as Bayern continued to turn the screw.
As the clock ticked down Guardiola brought on Arjen Robben. The Dutchman had a free-kick well saved, then shot from long range straight at Leno, while Muller's header from Alaba's cross was blocked.
The visitors, however, could find no way through and Hyypia's men held out for an excellent point, as Giulio Donati made sure of the result in stoppage time, heading Bastian Schweinsteiger's goalbound header off the line.