The in-form forward scored at the start of either half to set up the victory and become only the second man after Peter Meyer to register nine goals after five Bundesliga games.
He might have reached 10 had Philippe Coutinho not grasped the chance to open his Bayern account by converting the penalty he won just after the hour.
Kingsley Ehizibue saw red for the foul and Niko Kovac's men made their numerical advantage count, completing the rout with a fourth through Ivan Perisic.
Lewandowski struck in the third minute against RB Leipzig last weekend and did likewise here for his 10th goal of the season in all competitions.
Played in by Joshua Kimmich, the striker's finish deflected off Sebastiaan Bornauw's outstretched boot and bounced over Timo Horn.
Coutinho initiated the opener with a cute flick and soon curled a free-kick into the near post.
Cologne started to ask questions through Jhon Cordoba before Lewandowski found the top of the net from an awkward angle in first-half stoppage-time.
He made no mistake after the interval, rising high to nod in Kimmich's corner in the 48th minute.
There was more misery for Cologne on the hour as right-back Ehizibue bundled Coutinho to the floor in the box and was shown a straight red card.
The Brazilian dusted himself off and coolly converted twice, his first successful effort chalked off because of encroachment.
Kimmich then guided a curling effort against the upright but Bayern was not to be denied a fourth as winger Perisic fired across Horn in the 73rd minute.
There was time left for Manuel Neuer to make his own impressive contribution to the victory, the goalkeeper underlining his status as Germany's first choice when he parried Rafael Czichos' strike in the closing moments.
Kovac described the 1-1 draw at Leipzig as Bayern's "best performance" of the season and it appears his team is ready to produce more such showings.
While this was not a perfect display, it maintained the momentum of the midweek UEFA Champions League victory over Red Star Belgrade and bore hallmarks of a side that is starting to gel nicely.
Bayern travels to bottom-placed Paderborn, another newly promoted side, next Sunday (AEST). Cologne has an extra day to prepare for a home date with Hertha Berlin.