The Poland striker's ninth-minute opener meant the champion scored in a record 66 consecutive league games, a feat never before achieved in Germany's top tier.
Corentin Tolisso scored a fine second before two more Lewandowski goals in the second half secured a ninth league win in a row over Steffen Baumgart's side.
Fittingly, it was Lewandowski who set Bayern's latest goalscoring record, the striker side-footing past Marvin Schwabe from Thomas Muller's pass and a video assistant referee (VAR) check overruling an offside call.
The visitors doubled their lead in spectacular fashion, Tolisso controlling Muller's lay-off before rifling left-footed into the top-right corner from the edge of the box.
Cologne thought it had pulled a goal back through Mark Uth, but another VAR check showed an offside, and the hosts finished the half without another shot on target.
Marcel Sabitzer had an effort saved and Jamal Musiala's turn and shot clipped the outside of the post as Bayern stepped up the pressure after the interval.
Cologne offered a slight threat of a comeback with a good period of pressure, but it was promptly Lewandowski quelled 62 minutes in, Lewandowski drilling home his 22nd Bundesliga goal of the season after being played through by Leroy Sane.
The pair combined again for Bayern's fourth, Muller releasing Sane on a jinking run before he prodded through for Lewandowski to finish with aplomb.
The comfortable win stretched Bayer's lead at the top back to six points, Borussia Dortmund having closed the gap with a 5-1 thumping of Freiburg on Saturday (AEDT).
Cologne sits eighth on the table, two points off the top four.