The German league's bottom-placed side held on for a point as they frustrated die Roten, who have now slipped behind Monchengladbach in the standings
Freiburg were ready to give their all from the very start, and had their visitors on their heels for most of the first half. Other than a header from Holger Badstuber that was called offside, Bayern were rather impotent in the final third.
Instead, Freiburg took the initiative as well as the game to the Bavarians. On 15 minutes, Daniel Caligiuri made a fine run before finding Erik Jendrisek, who fired off target. Ten minutes later, Johannes Flum made a mazy run before Jerome Boateng's last-ditch challenge deflected his shot wide.
The only real chance Bayern managed to create before the interval came in the 42nd minute, as Thomas Muller showed stunning technique to volley Franck Ribery's cross. Baumann was well-positioned, however, to save the Germany international's shot.
Jupp Heynckes shuffled his line-up after the break, bringing Arjen Robben in for Rafinha, a move that saw Toni Kroos move into defensive midfield, David Alaba to left-back, and Philipp Lahm to the right.
And in the moments following the restart, the two sides traded fruitless attempts on goal. Badstuber came close with another header, shortly before Boateng again was forced to make an excellent challenge to stop Caligiuri. Ribery threaded a fine through-ball to Robben, but the substitute was unable to beat Baumann from a tight angle.
Play soon tightened as Bayern kept the majority of the possession, but were stymied in attack by Freiburg's impenetrable backline. One creative spell involving Ribery and Muller led to a half-chance for the visitors, but the final shot was blocked.
The hosts found counterattacking opportunities more rare in the second half, and were silent in the final third for a long spell, before Caligiuri nearly blasted home a winner on 84 minutes. However, Manuel Neuer made a superb save to deny the winger.
There were no late heroics from either side, and the game finished in a scoreless draw that saw Bayern end the day third in the Bundesliga table, four points behind leaders Dortmund, and one behind Monchengladbach. Freiburg move level with Augsburg and Kaiserslautern on 18 points, but remain last.