Bundesliga top scorer Lewandowski rifled in from a Thomas Mueller assist in the ninth minute to set a league record as Bayern have now scored in 66 consecutive Bundesliga matches.
With Dortmund having beaten Freiburg 5-1 on Friday to provisionally move within three points of the leaders, Bayern were eager to make sure of victory quickly.
They scored again when Corentin Tolisso beautifully combined with Mueller to thunder a shot into the top corner in the 25th.
The hosts, who were on a three-game winning run, tried to get back into the game and put the ball in the net through Mark Uth after the half-hour mark but it was ruled offside.
Lewandowski killed off the game just past the hour, chipping the ball past Cologne keeper Marvin Schwaebe to make it 3-0.
The 33-year-old Pole bagged his 23rd goal of the campaign, and his 300th in the Bundesliga having also played for Borussia Dortmund, when he slotted home from close range after good work by Leroy Sane 12 minutes later.
Lewandowski is second on the league’s all-time scorers list with only Bayern great Gerd Mueller ahead of him with 365 goals.
The Bavarians, chasing a record-extending 10th consecutive league title, have 46 points from 19 games with Dortmund in second place on 40.
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