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England captain Kane, who equalled a league record with at least two goals in four consecutive matches, has now netted 30 times in 24 Bundesliga games this season.

The visitors made a strong start with five efforts on goal before Dortmund scored against the run of play when Nico Schlotterbeck headed in Daniel Svensson's corner after 26 minutes.

But Kane was left unmarked in the 54th to tap home from a Serge Gnabry header before converting a penalty after 70 minutes to put the visitors ahead.

Dortmund, which was eliminated by Atalanta in the midweek UEFA Champions League play-offs, levelled through Svensson's superb 83rd-minute volley but the visitors snatched the three points when Kimmich blasted home a late volley of his own.

The win has moved Bayern a big step towards retaining the title.

The Bavarian side is 11 points clear of second-placed Dortmund with the Ruhr valley club's title hopes all but ended with 10 games remaining.

"To come from behind [and win] this is a special feeling right now," Kane said after the match.

"We said at half-time to just stay came, to play our football. We knew they might get a little bit tired after playing the game in midweek, and we used that to our advantage.

Despite Bayern now being 10 points clear at the top of the table, Kane is not ready to relax.

"It puts us in a great position, but it's not over yet. We had an 11-point before and you did see how quickly it can change – it went to six pretty quick – so we can't get carried away, but you have to enjoy nights like tonight."

Bayern boss Vincent Kompany also insisted his side will not let up, despite its healthy lead over Dortmund in the title race.

"We now have an 11-point lead. We've scored 88 goals. Why stop now? We're going full throttle," the Belgian said.

"The game was a great advert for the Bundesliga. The momentum, the intensity, the scoreline, the 80,000 spectators. It was simply brilliant.

"Dortmund really wanted to take the opportunity; you could feel that throughout the match. That's understandable.

"But we didn't just sit back and absorb pressure; we always tried to create our moments, and in my opinion, they were good moments. Both teams had the desire to push forward."

Dortmund head coach Niko Kovac hailed the performance of Bayern's Kimmich, labelling him as the decisive factor in the match.

"In the end, the world-class quality of Joshua Kimmich was simply decisive," Kovac said.

"How he assisted the first goal and scored the third – that was the key.

"We wanted a good result going into the break, and we achieved that. In the second half, it became a real shootout.

"Bayern this season is offensively absolute world-class – almost everyone concedes multiple goals against them.

"Defensively, we could have done better. Offensively, I was satisfied with my team. Unfortunately, it wasn’t enough.

"We now have more free days and want to continue developing. For us, it’s about staying close to Bayern in the table in a composed manner."

Dortmund will now have a week off before travelling to Koln on 8 March (AEDT), but the Bundesliga title is perhaps beyond it now.