The Bavarians were punished for a slow start as Christian Gunter produced a precise and powerful effort to give the hosts an early lead.
Mathys Tel pulled the visitors' level in the 35th minute, before Jamal Musiala scored his seventh league goal of the season to give Bayern a slender lead.
Just as the Bavarians seemed to be on course to claim maximum points, Holer found the net in the 87th minute to rescue his side a precious point and extend Bayern's winless away run to four competitive matches.
The result leaves second-placed Bayern seven points adrift of leaders Bayer Leverkusen, who will have the chance to extend the gap to 10 points when they face Koln on Sunday.
Despite losing four of their previous five league matches, Freiburg made a confident start in their home meeting with the reigning champions.
Gunter required just 13 minutes to give the hosts the lead just seconds after Roland Sallai had forced a save from Manuel Neuer and rattled the woodwork with his acrobatic rebound.
Freiburg kept the ball alive following Sallai's double chance, and it eventually fell into the path of Gunter, who unleashed a fierce shot into the bottom corner.
Just moments later, the 31-year-old then threatened to add a second, but he was ultimately denied by the imposing figure of Neuer.
The Bayern goalkeeper was then left relieved when Vincenzo Grifo curled the ball wide after cutting inside onto his favoured right foot.
Following an underwhelming opening half hour, Thomas Tuchel's side pulled themselves level thanks to a piece of brilliance from Tel, who picked the ball up on the edge of the box, before curling an unstoppable effort out of the reach of Noah Atubolu.
After seeing Tel restore parity before the break, Harry Kane went close to completing the turnaround in the early stages of the second half, driving a low shot inches wide of the Freiburg goal.
Bayern continued to pile on the pressure as Musiala saw his strike pushed wide by Atubolu, before Kane saw his goalbound effort cleared off the line from the subsequent corner.
The visitors' persistence ultimately paid off in the 75th minute when Musiala demonstrated his close control to evade a number of Freiburg defenders and bend the ball in off the far post.
After completing the turnaround, the Bavarians took their foot off the gas as they looked to see out the rest of the game, but their complacency proved costly as Holer latched onto a bouncing ball to hook a left-foot strike past the helpless Neuer.
Although Freiburg are now winless in six league games, the ninth-placed side will be pleased to take a point off the reigning champions, moving them to within four points of the top six.
As for Bayern, they will have to quickly pick themselves up for Tuesday's Champions League meeting with Lazio at the Allianz Arena, where they will attempt to overturn a one-goal deficit.