The result left champions Bayern, who have 54 points from 24 league matches, seven behind leaders Bayer Leverkusen, who have 61 and can pull further away with a win over Cologne on Sunday.
Bayern, preparing to host Italy's Lazio in their Champions League last 16 second leg next week, suffered a nightmare start to their record 2 000th Bundesliga game with the hosts finding spaces to attack.
The Bavarians had keeper Manuel Neuer to thank for keeping them in the game with a string of outstanding saves early in the first half.
Freiburg took their chances against a crisis-hit Bayern, who will part ways with coach Thomas Tuchel at the end of the season, and were rewarded with a 12th minute lead.
Neuer first spectacularly palmed a Roland Sallai header away, then saw the Hungarian's rebound bicycle kick bounce off the post before Christian Guenter rifled in.
The hosts had half a dozen chances to score again in a strong half hour before Bayern hit against the run of play with an unstoppable long-range shot from Mathys Tel in the 35th.
The visitors looked sharper after the break and came close with Jamal Musiala and Harry Kane before the former launched a solo run down the left, cut into the box and curled a low shot past the Freiburg keeper to compete their comeback.
Freiburg, however, struck in the 87th with Hoeler bagging the late equaliser after a fine turn and shot in the box. Bayern have now managed just one win from their last four league games.