Despite being the Bundesliga's top scorers, Bayern failed to register a single shot on goal in the first half in a record first for the German giants.
At the other end, Florian Wirtz brought a good save out of goalkeeper Manuel Neuer, before Jeremie Frimpong headed the rebound against the crossbar. Nathan Tella then went closest to breaking the deadlock, only for his effort to crash against the frame of the goal soon after.
The former Southampton man was a whisker away from scoring against Vincent Kompany's men - who put in a strong rearguard effort - but his acrobatic effort went the wrong side of the post.
Hiroki Ito was then in the right place at the right time to head Tella's header off the line as the visitors struggled to string passes together in the face of Leverkusen's sustained pressure.
Wirtz should have won it at the death for the hosts, who looked like the league leaders at BayArena, but his side could not break Bayern's stubborn resistance.
Bayern, who didn't register a shot on goal until deep into the second half, remain eight points clear of second-placed Leverkusen with 14 games of the league campaign remaining.