After suffering a humbling 6-2 defeat in the reverse fixture, Freiburg were hoping to be far more competitive as they faced the runaway league leaders.
And with a quarter-hour played, they had a golden opportunity to open the scoring when Jan-Niklas Beste pulled the ball back for Philipp Treu, who should have done better than to side-foot a first-time effort wide of the mark.
The hosts soon called Manuel Neuer into action, forcing the shot-stopper to palm away on two occasions as he thwarted Lucas Holer’s close-range volley before pushing away a Philipp Lienhart diving header, albeit each from offside positions.
Bayern had struggled to produce any clear-cut chances as the interval approached, with Freiburg continuing a trend, having conceded a league-low five first-half home goals this season.
However, the visitors offered a reminder of their attacking threat ahead of the break, as Lennart Karl tested Noah Atubolu with a low strike before failing to adjust as he skied a close-range bouncing ball.
Serge Gnabry then drilled a strike from range narrowly off-target, keeping the scores level heading into half time.
Parity lasted a matter of moments after the restart, though, with Johan Manzambi bending a delightful shot from distance beyond a motionless Neuer to put the hosts in front.
Bayern had not yet lost a Bundesliga game in which they had conceded first this season (W5, D3), but they were enormously fortunate not to find themselves further behind as Holer wasted two excellent chances, blazing over inside the box before stroking agonisingly past the post.
Substitute Michael Olise mistimed his finish from point-blank range to let Freiburg off the hook, and they made the most of that let-off, doubling their lead with 19 minutes to play.
Neuer’s miscalculated attempt at an intervention from a corner left Holer with the simple task of tucking home the loose ball.
However, Bayern pushed hard for a response, and Tom Bischof played a significant role. He first halved the deficit with a well-struck drive past Atubolu in the 81st minute, before eventually levelling the game in stoppage time with another fierce effort.
Incredibly, Bayern snatched all three points with a 99th-minute winner from Karl, who tapped home at the back post to send the away fans delirious.
As a result, Bayern stay comfortably top of the table, just one goal away from breaking their own 1971/72 record of 101 scored in a single German top-flight campaign.
Vincent Kompany’s side now turn their attention to the quarter-finals of the UEFA Champions League, in which they face Real Madrid in midweek.
As for Freiburg, they’ll be focused on their UEFA Europa League encounter with RC Celta de Vigo, with Julian Schuster’s side sat eighth in the Bundesliga.