The contest was over before half-time as Eugen Polanski, Mohamed Zidan and Nicolai Muller scored in an 18-minute spell in the first half, condemning Cologne to their fourth defeat in five games during which they have conceded 17 goals.
Adam Szalai added the fourth while Cologne forward Lukas Podolski was hit in the face by a small object thrown from the crowd in the first half. He was not hurt and continued playing.
Hertha defender Hubnik turned Garra Dembele's shot into his own net after seven minutes and the Malian also set up Freiburg's second for Sebastian Freis after the hour.
Mike Hanke scored twice after the break to put Gladbach ahead but Brazilian defender Naldo headed Bremen's equaliser in the 74th minute.
Although Peszko has publicly apologised after Saturday night's incident, in which he was widely reported to have become he become drunk and quarreled with a taxi driver who took him to a police station, he was left out of the Cologne team.
"We played reasonably well until we conceded the first goal," said Cologne goalkeeeper Michael Rensing. "Then we suffered four goals again. That for me is inexplicable."
The three-times German champions were quickly in more trouble as Adam Szalai's theatrical fall earned Mainz a penalty which was converted by Peszko's fellow Pole Eugen Polanski in the 18th minute.
Egypt forward Mohamed Zidan drilled the ball emphatically home in the 32nd minute after Muller teed up his shot, then Muller himself got on the end of Eric Maxim Choupo-Moting's measured pass to
