The home fans paid tribute to Harry Kane, the first Bayern player to win the Ballon d’Or since 1981, but it was their other attacking superstar who went close early on, as Michael Olise’s snapshot from the edge of the box thumped against the right post.
But Dortmund gave a good account of themselves, and Jobe Bellingham’s shot from 20 yards required a strong hand from Jonas Urbig to turn it away.
Ismael Saibari then broke away for Bayern, only for Gregor Kobel to rush out and get in the way of his prodded effort.
The first-half action, though, really exploded into life in its final 15 minutes, with Bellingham burying what he thought was his first-ever Bundesliga goal, only for it to be chalked off due to Carney Chukwuemeka obstructing Urbig.
That made Bayern’s opener a couple of minutes later a bitter pill for the visitors to swallow, with Konrad Laimer racing onto Olise’s flicked pass and finishing past Kobel at the second attempt.
Dortmund’s start to the second half was promising, but Bayern were subsequently awarded a penalty when Kane’s volleyed effort was deflected away by Felix Nmecha’s hand.
However, having scored 25 of 26 Bundesliga penalties prior, Kane’s first after winning the sport’s biggest individual gong ended up firing back off the crossbar.
That lifeline was welcomed with open arms by Dortmund, who rewrote the script moments later when Chukwuemeka rushed into the box and laid it off for Serhou Guirassy, who took one touch and slotted into the near corner.
Unfortunately for the thousands of travelling fans, parity was short-lived. Joshua Kimmich’s cross found Kane completely unmarked at the far post, and the England captain headed it across goal for Dayot Upamecano to bundle in.
Bayern missed a few more chances after that, and they were again punished when it fell for Fabio Silva in the area with just over a minute remaining, with the substitute finishing brilliantly into the far post.
Lennart Karl’s shot onto the bar meant Bayern failed to take the lead again before the final whistle, contributing to a record of one win in their last four home Bundesliga matches against Die Borussen.
That late equaliser displayed Dortmund’s mettle and squad depth, and outlines their intentions to take their challenge for a first Meisterschale since 2011/12 all the way this season.
Flashscore Man of the Match: Konrad Laimer (Bayern Munich)