Bayern, chasing an eighth successive title, have 46 points from 22 games, one ahead of RB Leipzig who had gone top with a 3-0 win over Werder Bremen on Saturday. Cologne are 14th with 23 points and have a six-point cushion over the relegation playoff spot.
"We just went to sleep for the first few minutes," said Cologne goalkeeper Timo Horn.
Bayern's opening goal came after a throw-in led to a quick exchange of passes which freed Lewandowski to fire his shot into the roof of the net for his 23rd league goal of the season and 36th in all competitions.
Two minutes later, Bayern sliced open the Cologne defence with incisive passing and Coman placed his shot under Horn.
It got worse for the hosts when a corner flew over the Cologne area and landed at the feet of Gnabry, who took it past a defender and drilled his shot into the bottom corner.
Bayern, who were sixth in early December, had 18 shots on goal in the first half and could easily have doubled their tally as Gnabry and Joshua Kimmich hit the Cologne woodwork and Thomas Mueller scooped another effort over the crossbar.
Juventus offer star duo to Manchester United in attempt to re-sign Pogba – Euro Papers
Cologne pulled themselves together after the break and Jhon Cordoba twice had the ball in the net but both efforts were ruled out for offside, the first after a long VAR delay.
But it was Bayern who scored again when Gnabry collected the ball in midfield, ran into the heart of the Cologne defence and curled his effort past Horn in the 65th minute.
Uth pulled one back in the 70th minute and Bayern goalkeeper Manuel Neuer needed to make several to keep the hosts at bay.