Ballon d'Or winner Harry Kane missed a penalty and hit the post for Bayern Munich as Borussia Dortmund snatched a last-gasp equaliser through Fabio Silva for a 2-2 draw in a thrilling Klassiker on Saturday that kept the teams level on points at the top.

In a frustrating match for home fans, Bayern twice took the lead, missed a penalty, hit the post four times and had three players -- Ismael Saibari, Serge Gnabry and Michael Olise -- taken off injured. The Bavarians play Atletico Madrid in the Champions League next week.

Kane, who claimed his prize at a ceremony in London on Monday, was an unused substitute in the 6-1 German Cup second-round demolition of Magdeburg on Wednesday before missing from the spot with Bayern 1-0 up.

Silva snatched the equaliser in the 89th minute to leave both teams on 18 points, with Bayern top on goal difference.

"Mixed emotions. We're really pleased with the performance, especially this second half," said Bayern assistant coach Aaron Danks, who is in charge with head coach Vincent Kompany recovering from illness.

"So ultimately we'll feel disappointed that we haven't got the win. We had the right moments for us, and it just didn't go our way today."

Danks said it was too early to determine the extent of the injuries but said Saibari's ankle issue looked serious.

In a rollercoaster first half, Bayern hit the woodwork through Michael Olise and wasted a golden chance for Ismael Saibari, who was injured and later left the stadium on crutches, before the visitors had a goal overruled by VAR.

Bayern struck in the 38th minute thanks through Konrad Laimer's goal on the rebound, after his first effort was blocked by Dortmund's Gregor Kobel.

Full back Laimer was more threatening than Kane, who sent his 56th-minute spot-kick against the crossbar.

Dortmund scored through Serhou Guirassy on the hour mark but their joy only lasted six minutes as Dayot Upamecano tapped in a Kane assist from close range.

Kane's low shot bounced off the post before Silva bagged the equaliser. Bayern's Lennart Karl still had time to see his shot in stoppage time bounce off the crossbar.