Leon Goretzka thought he had put Bayern ahead in the 50th minute but his effort was ruled out for offside and Leipzig were able to frustrate the league leaders for the remainder of the game, carving out a few notable chances of their own. Dortmund goes to Borussia Monchengladbach on Saturday at 9:30 a.m. ET, while Bayern hosts Eintracht Frankfurt.
Bayern, who needed a win to make sure of a record-extending seventh consecutive league title, are on 75 points.
Dortmund, who looked dead and buried after slipping four points behind last week, enjoyed the rub of the green as they stumbled to victory over Duesseldorf.
A howler from stand-in goalkeeper Marwin Hitz allowed Oliver Fink to equalise within seconds of the restart, but Thomas Delaney restored the lead for Dortmund on 53 minutes.
Thomas Delaney put the hosts back in front on 53 minutes, but a photo-finished ensued with Mario Gotze grabbing the victor in added time and Dawid Kownacki the consolation seconds later.
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"We have to give everything next weekend and of course it depends on Bayern", Pulisic said.
Hanover 96 and Nuremberg were relegated due to VfB Stuttgart's 3-0 win against Wolfsburg, which ensured them a 16th-place finish and a relegation/promotion playoff with the third-placed team from the second tier.
Gonzalo Castro broke the deadlock for Stuttgart in stoppages of the first stanza while Anastasios Donis and Daniel Didavi sealed the three points in the second stanza.
Also, Werder Bremen won at Hoffenheim 1-0, and Hertha Berlin won at Augsburg 4-3 thanks to Salomon Kalou's goal in injury time.
Johannes Eggestein's first-half goal condemned RB Leipzig-bound coach Julian Nagelsmann to defeat in his last home game in charge of Hoffenheim. "We still have a chance to win the title".