Top scorer Robert Lewandowski scored twice, including a second half penalty, to guide the German champions to a crucial 3-2 victory at title rivals Borussia Dortmund on Saturday and a four-point lead at the top of the Bundesliga.

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The Pole -- ranked the top striker in ESPN FC 100 -- opened his account in the in the ninth minute to level after Dortmund had taken an early lead through Julian Brandt, and then converted a 77th minute spot kick to seal victory with his 16th goal of the campaign.

Kingsley Coman had put Bayern in front a minute before the break before Erling Haaland equalised for the hosts with a superbly curled effort in the 48th.

In an action-packed encounter, Dortmund coach Marco Rose was sent off with a second booking for dissent following the penalty decision.

Bayern, chasing a record-extending 10th league crown, move up to 34 points with this sixth straight league win over their rivals, leaving Dortmund in second place on 30. Bayer Leverkusen are in third place on 27.

"I think we deserved to win but I also understand the discussions over the two penalty situations," Bayern coach Julian Nagelsmann said.

Dortmund were fuming about the penalty decision in favour of Bayern after having been denied a VAR review in a penalty claim of their own earlier.

"It was a very tight game that was worthy of its reputation. We could have scored more in the first half," Nagelsmann said. "Dortmund did it well early in the second half but we found our rhythm again and had good control."

The game instantly lived up to its billing with Haaland charging through after two minutes and keeper Manuel Neuer clearing the ball just in time.

Brandt did it better a little later, peeling off his marker and thundering in for the lead.

Bayern drew level four minutes later when defender Mats Hummels clumsily tried to clear a high ball before Thomas Mueller got it but the ball fell for Lewandowski.

In a hugely entertaining, end-to-end first half in front of a limited 15,000 crowd, both teams had their share of opportunities, with Haaland firing just wide on the half-hour mark and Coman twice coming close for the visitors.

The winger did get on the score sheet a minute before the break when after another sloppy Dortmund clearance the Frenchman fired in to beat keeper Gregor Kobel.

Three minutes after the restart it was Dortmund's turn to come back, with Jude Bellingham laying the ball off for Haaland on the left and the Norwegian bagging his 51st goal in his 51st Bundesliga match with a delightful curled shot into the top corner.

But the controversial Hummels handball decision following a lengthy VAR review allowed Lewandowski to score his 26th goal in all competitions against his former club.