They are four points clear of Borussia Monchengladbach in second.
Wait. What?! A quick glance at the table shows that Dortmund are top of the league after 11 matches and Bayern are seven points adrift!
Dortmund have yet to confirm Burki's withdrawal, but in his absence Marwin Hitz, 31, who is also a goalkeeper with the Switzerland national team, would step in.
Dortmund levelled from the penalty spot through Marco Reus after he had been fouled by Bayern keeper Manuel Neuer. The domination finally paid off in the 26th minute as Lewandowski scored against his former club, nodding home from a Serge Gnabry cross.
Then Achraf Hakimi squared the ball for Reus, who somehow sidefooted over the bar.
The lead, though, did not last long and Bayern were back in front on 52 minutes. Alcácer, though, failed to convert due to Jérôme Boateng's superb saving tackle and Jacob Bruun Larsen sent the rebound over.
Dortmund completed the turnaround on 73 minutes when Franck Ribery was caught in possession by Sancho, who fed Axel Witsel.
Bayern looked for a late equaliser, which nearly arrived when a free-kick from Kimmich was inadvertently headed back towards his own goal by Reus, the ball dropping just past the post.
Lewandowski got the ball in the back of the net for Bayern deep in stoppage time with a back-heel but he was flagged offside as the visitors went down 3-2 to a spirited Dortmund.