Robert Lewandowski scored twice as Bayern Munich opened up a four-point lead at the top of the Bundesliga with a 3-2 win at second-placed Borussia Dortmund on Saturday.

Julian Brandt and Erling Haaland scored Dortmund's goals at Signal Iduna Park, but Lewandowski netted and converted the winning penalty, either side of a Kingsley Coman goal.

Dortmund coach Marco Rose was shown a red card for arguing with the referee after a Mats Hummels handball led to Lewandowski converting the key spot-kick 12 minutes from time.

"In the first half, we should have led by more and in terms of how we played, I'm not sure we deserved to win," said Bayern forward Thomas Mueller.

"But in terms of fighting, we were there."

This was Bayern's seventh straight win over Dortmund, including five Bundesliga victories and two German Super Cup triumphs.

Dortmund were unhappy to not be awarded a penalty after Marco Reus appeared to be fouled just before Lewandowski's crucial spot kick.

"We always had the feeling that we could win. That's why it's doubly bitter that we lost like that," fumed Reus.

Dortmund forged ahead in the fifth minute when Brandt, who was later stretchered off after a clash of heads, slammed in a superb shot.

A Hummels mistake led to Lewandowski equalising four minutes later against his former club when the Poland striker motored onto a Thomas Mueller pass and fired home.

Bayern capitalised on another Dortmund error when Coman's excellent strike put the visitors in front before half-time.

Just 120 seconds after the break, Dortmund were level when Haaland shot past diving Bayern goalkeeper Manuel Neuer after Dayot Upamecano cheaply gave away possession.

Dortmund were unlucky not to be awarded a penalty when their captain Marco Reus appeared to be fouled by Lucas Hernandez.

At the other end, Hummels was again at fault when VAR confirmed his handball, to Rose's fury, and Lewandowski made no mistake.

It was Lewandowski's 22nd goal in 15 Bundesliga games against Dortmund, who he left in 2014.

Bayern midfielder Corentin Tolisso fired wide of an open Dortmund goal during 10 tense minutes of stoppage time.

Earlier, Czech Republic striker Patrik Schick scored four second-half goals as third-placed Bayer Leverkusen romped to a 7-1 thrashing of bottom club Greuther Fuerth.

Schick became the first Leverkusen player to score four goals in one half of a Bundesliga match.

"In the first half I didn't have a single shot at goal. The second half was like opening a bottle of ketchup," Schick quipped.

Amine Adli and Edmond Tapsoba scored early goals for Leverkusen before Fuerth pulled a goal back from Jeremy Dudziak.

Schick was then involved in the next five Leverkusen goals as the hosts ran riot.

He set up Ecuador's Piero Hincapie just before the break, then fired in four goals in just 27 minutes -- two with his left foot, one with his right and a header.

Schick has now scored 12 times in 11 league games this season and trails only Lewandowski, who has netted 16 goals, in the scoring charts.

Wolfsburg crashed to a 3-0 defeat at Mainz ahead of Wednesday's all-or-nothing Champions League clash at home to Lille.

Wolfsburg never recovered from conceding a goal by forward Jonathan Burkardt after just 68 seconds and were 2-0 down after only four minutes when Anton Stach scored from outside the box.

To compound Wolfsburg's misery, their French defender Maxence Lacroix scored a late own goal.

Hoffenheim climbed into the top four with a 3-2 home win over Eintracht Frankfurt, whose three-match winning streak was ended.

Colombia striker Rafael Borre gave Frankfurt an early lead, but goals by Dennis Geiger, Georginio Rutter and Diadie Samassekou put Hoffenheim in command.

Substitute Goncalo Paciencia scored Frankfurt's second to set up a tense final 20 minutes, with empty stands in Sinsheim due to high numbers of Covid cases in the region.