The Bavarians, chasing a record-extending 10th consecutive league title, bounced back from last week’s loss to Borussia Moenchengladbach and have 46 points from 19 games with Dortmund in second place on 40.
Bundesliga top scorer Lewandowski rifled in from a Thomas Mueller assist in the ninth minute after Cologne’s Ondrej Duda had lost possession, to set a league record as Bayern have now scored in 66 consecutive Bundesliga matches.
It was also the first of three goals for the Pole, who has so far netted 23 times in the league this season.
“We are happy and grateful to have him in our team,” Bayern keeper Manuel Neuer, back from his COVID-19 infection, said.
“We have a lot to thank him for because he is just a machine in the box and in keeping possession. His finishing is unique.”
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.
The champions, who had lost 2-1 against Gladbach, scored again when Corentin Tolisso, also back from a COVID-19 infection, 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.
Lewandowski is second on the league’s all-time scorers list with only Bayern great Gerd Mueller ahead of him with 365 goals.