Bayern Munich could not convert possession into goals in Freiburg, and the Bavarians were made to pay late in the game. Freiburg recovered a 1-1 draw through young substitute Nicolas Höfler.
Bayern got the Bundesliga action rolling well ahead of schedule on Tuesday, playing an early game before Friday's European Super Cup against Chelsea.
Bayern coach Pep Guardiola appeared to have more than one eye on the game against the Premier League side, now coached by his old nemesis from his days in Spain, Jose Mourinho. Guardiola left out several first-choice players, including captain Philipp Lahm, front man Mario Mandzukic and the wide pairing of Arjen Robben and Franck Ribery.
Nevertheless, Bayern's star-studded "reserves" - 10 of whom had senior international caps to their names - dominated most of the match, enjoying in excess of 70 percent of possession.
The game was proceeding according to plan just after the half-hour mark, when Xherdan Shaqiri capped an excellent move down the right. Thomas Müller floated the ball across and Shaqiri crashed his volley past Oliver Baumann in the Freiburg goal.
No killer blow for Bayern
In the second half, Bayern continued to monopolize the ball, but only to generate a few more chances than their hosts. The decisive period of play took place in the moments before substitute Sebastian Höfler's equalizer.
In the space of around 45 seconds, Freiburg keeper Oliver Baumann kept out three one-on-ones, from Toni Kroos, Thomas Müller and then Müller again. They were probably the three clearest chances of the game, and any one would have been the insurance policy the Bavarians needed.
About a quarter of an hour later, Höfler scored almost a carbon copy of Shaqiri's earlier goal - an unstoppable left-footed volley from a cross from the right. The only difference was that where Shaqiri went for power, Höfler placed the ball out of Manuel Neuer's reach.
Höfler is the first non-Bayern player to put the ball past Neuer this Bundesliga season. The only other goal Bayern conceded was an own-goal from defender Dante against his old club Borussia Mönchengladbach on opening day.
The two dropped Bayern points mean that Borussia Dortmund, Bayer Leverkusen and Mainz could all move top of the table with wins this weekend.