Bayern Munich's Robert Lewandowski, left, celebrates after scoring the opening goal during their German Bundesliga game against 1. FC Cologne in Munich on Saturday. Photo: Matthias Schrader/AP

BERLIN – Bundesliga top scorer Robert Lewandowski scored twice to equal a 51-year-old record as champions Bayern Munich demolished Cologne 4-0 on Saturday to move up to second place in the standings.

Unbeaten Leipzig stayed top of the table on 13 points, two ahead of Bayern, after beating Werder Bremen 3-0 for their fourth win in five games.

Poland striker Lewandowski grabbed Bayern's first two goals and, after Cologne's Kingsley Ehizibue was sent off, Philippe Coutinho converted a penalty to make it 3-0 and Ivan Perisic completed the rout with a low shot.

Lewandowski, who has been Bundesliga top scorer four times in the last six seasons, has netted nine times in the opening five league matches, equalling a record set by Borussia Moenchengladbach's Peter Mayer in the 1967-68 season.

He grabbed Saturday's first goal after three minutes to equal a club record set by Carsten Jancker in the 2000-01 campaign of scoring in each of the opening five matches of the season.

Lewandowski added another straight after the restart and the striker has now scored 11 goals out of Bayern's 18 in total in all competitions this season.

Coutinho made sure of the three points from the penalty spot and the Brazilian set up Perisic with a fine through ball for the fourth to complete a winning week for Bayern after their 3-0 Champions League group victory over Red Star Belgrade.

"Four-nil sounds like a big score but we could have added one or two more," said Bayern coach Niko Kovac. "Seven goals this week is something we can build on.

"We delivered a good performance today, especially after having only 72 hours to recover from Wednesday."

Leipzig had Bremen on the back foot from the start and Willi Orban headed in for the lead from a corner in the 13th minute. Marcel Sabitzer doubled it in the 35th with a fine free kick.

Werder tried to come back after the break but it was the visitors, fresh from their opening Champions League group win at Benfica in midweek, who scored again, with Marcelo Saracchi in the 83rd.

Borussia Dortmund, on nine points, travel to Eintracht Frankfurt on Sunday.