Dortmund twice blow lead, save point
Bayern led second-place Leverkusen by 10 points with a game in hand, while Dortmund was another four points off the pace.
Freiburg midfielder Felix Klaus scored in the last minute as his side twice came from behind to climb provisionally out of the relegation zone.
''We still have an incredibly long way to go,'' Freiburg coach Christian Streich said.
Lars Bender scored with Leverkusen's first shot in the fourth minute and Admir Mehmedi equalized with a fine strike in the 27th before Simon Rolfes restored the visitors' lead eight minutes later.
Jonathan Schmid's free kick squeezed inside the near post in the 53rd, thanks to a light deflection from Leverkusen striker Stefan Kiessling on his 30th birthday, and Klaus scored the winning goal on a counterattack.
''Freiburg were dangerous,'' Leverkusen coach Sami Hyypia said. ''We tried to win, then came the counter.''
Dortmund endured an afternoon to forget as the side's bad luck with injuries continued. Poland midfielder Jakub Blaszczykowski sustained suspected cruciate ligament damage to his right knee in the third minute.
''The opening period was overshadowed by Blaszczykowski's injury,'' said Dortmund coach Juergen Klopp, who has also had to contend with long-standing injuries to Ilkay Gundogan, Mats Hummels, Lukasz Piszczek and Neven Subotic.
Sven Bender headed home side Dortmund in front in the fifth - one minute after his twin opened the scoring for Leverkusen - but conceded an own goal in the 56th, when he deflected Andre Hahn's cross into his own net.
Nuri Sahin restored Dortmund's lead from a free kick in the 66th, only for South Korea midfielder Ji Dong-won, who will join Dortmund next season, to score Augsburg's equalizer in the 72nd just two minutes after going on as a substitute.
''You could see we'd set our sights high,'' Klopp said. ''But you could also see that that can lead to tension.''
Elsewhere, Nuremberg defeated Hoffenheim 4-0 for its first win of the season, Hannover won 3-1 at Wolfsburg for its first away win, and Mainz earned a 2-1 win at Stuttgart.
Alexander Meier's 36th-minute strike against the run of play was enough for Eintracht Frankfurt to defeat Hertha Berlin 1-0 in the late game.
The visitors might have had a penalty with some 20 minutes remaining, when Carlos Zambrano appeared to catch Ronny in the face with his elbow.
The referee didn't see it, however, and booked the Hertha midfielder for protesting.
Nuremberg coach Gertjan Verbeek had vowed not to shave until his side finally won in the league.
''I'm very happy with the win, also that the beard is shaved,'' the Dutchman said. ''It was important for us to take the lead.''
United States international Timmy Chandler opened the scoring with a deflected shot in the 24th, before two goals from Josip Drmic and another from Daniel Ginczek gave Nuremberg its first Bundesliga victory at the 18th attempt this season.
Belgian midfielder Kevin de Bruyne made his debut for Wolfsburg following his switch from Chelsea for a reported 22 million euros ($30 million).
Artjoms Rudnevs scored on his Hannover debut in the 28th, and Leonardo Bittencourt added two more in the 50th and 72nd for Hannover's first away win of the season in Tayfun Korkut's first game in charge. Ivica Olic had pulled Wolfsburg level in the 35th.
Korkut's predecessor, Mirko Slomka, who was fired during the winter break, watched from the stands.
In Stuttgart, Mohammed Abdellaoue's 11th-minute opener for the home side was canceled when Shinji Okazaki seized on a mistake from Japan teammate Hiroki Sakai to score against his former side in the 39th.
Mainz substitute Benedikt Saller snatched the winning goal in the 87th.
''The bottom line is that it's a lucky win,'' Mainz coach Thomas Tuchel said. ''But it's one of our qualities, to wait, to lurk.''