An early goal by Paraguayan striker Roque Santa Cruz and a second- half equalizer by Fredi Bobic were overshadowed by foul after foul which referee Hartmut Strampe proved unable to control, as Bayern withstood a second-half battering from a Dortmund lacking ideas.
Bayern defender Bixente Lizarazu was sent off after half an hour and playmaker Steffen Effenberg ten minutes into the second half, while the side saw what was a Bundesliga record for the club of eight yellow cards.
"I've never seen a match which the referee made so many mistakes - he must have made 50," was the terse comment of Bayern manager Uli Hoeness, while players from both sides joined the criticism chorus.
The result left Bayern on 50 points, with Dortmund on 49, in third position because of a two-goal disadvantage in the averages against second-placed Bayer Leverkusen, who earlier beat Frankfurt 3-1.
Bochum meanwhile kept their survival chances alive with a fine 4-2 win away at 1860 Munich, Werder Bremen put the brakes on Hertha Berlin's title challenge with a 3-1 win, Cologne and Unterhaching parted 1-1, and Freiburg and Hamburg had a goalless draw.
Santa Cruz, back after a lengthy period of injury, hit his sixth- minute goal off a brilliant piece of play down the left by Lizarazu, who managed a cross which the young Paraguayan was able to tap home.
Good moves followed from both sides - particularly from Dortmund via Czech playmaker Tomas Rosicky - and plenty of initial pushing and shoving including one incident where Bayern's Giovane Elber and Dortmund's Otto Addo squared up, and both saw the yellow card.
That proved a signal for more yellow cards to rain in a purple patch that saw Lizarazu sent off on the half hour for a second bookable offence as he crudely dragged down Rosicky who was making a break down the right.
Tempers promptly flared again after the break when a Fredi Bobic equaliser for Dortmund was ruled offside - replays showed it was a regular goal - then a Dede goal minutes later was also ruled offside.
Fredi Bobic's 52th minute goal finally brought a positive eruption from the 68,000 Dortmund crowd - a beautiful cross from the right by Lars Ricken struck home as Bobic fended off a strong challenge from Samuel Kuffour.
Three minutes later Bayern were down to nine men as their skipper Steffen Effenberg was sent off for a crude body check on Evenilson.
From then on the flow was in only one direction - with the Bayern defence taking one battering after another, with Dortmund's frustration crowned in the last minute when a Rosicky free kick hit the inner woodwork and bounced into the arms of keeper oliver Kahn.
By the time the ill-tempered affair was over, Bayern's yellow card collection had risen to eight, while Dortmund's Evanilson also saw red in injury time for a foul on Paulo Sergio.
Saturday's results - with Kaiserslautern and Schalke due to play Sunday - mean just four points separate Bayern, Dortmund, Leverkusen, Hertha Kaisterslautern and Schalke as all jostle for the title.
Good work on the right by Paulo Rink gave Leverkusen an early lead against Frankfurt, his cross finding a poorly-marked Ulf Kirsten's left boot to pound the ball home after 20 minutes.
Chinese international Chen Yang hit Frankfurt's 58th-minute equaliser as the side's hopes were temporarily revived under new coach Friedel Rausch, brought mid-week in to stave off relegation.
But then Leverkusen's Brazilian signing Lucio headed home off a corner in the 67th minute, and added his second in the 82nd minute to dash the home sides' hopes and send them into the drop zone.
Bremen, at home to high-flying Hertha Berlin after upsetting Bayern last week, did another demolition job with an early goal by the Peruvian striker Claudio Pizarro, followed by another in the 56th minute, delicately chipping home off the rebound.
Thorsten Frings hit the late third goal for Bremen that clinched things after Andreas Schmidt had scored in the 49th minute for the visitors, latching onto an unfortunate rebound from Bremen's Dutch defender Frank Verlaat.
The win kept alive Bremen's UEFA Cup chances for next season, lifting them into seventh spot after a fine pair of wins in as many weeks.
Goals from Christian Timm gave Cologne early hopes of a win over stragglers Unterhaching, who increasingly look relegation-bound after only their second season in the top division.
But then Markus Oberleitner hit the equalizer for Unterhaching just 40 seconds into the second half, leaving the side from the
(dpa)