The Polish champions' sluggish start to the season has led to speculation about coach Jacek Zielinski's future at the club, with former Barcelona and Spain striker Jose Maria Bakero being linked with the job.
But after falling behind to a strike from Pawel Brozek, Poznan hit back with a 52nd-minute equaliser from Dimitrije Injaca and further goals by Siergiej Kriwiec, Semir Stilic and late substitute Mateusz Mozdzen.
Poznan are still lying only 14th in the table but, having been beaten 3-1 at the City of Manchester Stadium a fortnight ago, will have their spirits raised for the Blues' visit this week.
Juventus idol Alessandro Del Piero scored a club record 179th Serie A goal to gain a 2-1 victory over Milan in the San Siro for Juve, who will host City's final group game in Turin next month.
Del Piero pounced with 25 minutes left, after Mohamed Sissoko had mis-hit a shot, to top Giampiero Boniperti's mark for Juventus and earn the visitors three priceless points.
Fabio Quagliarella headed the fourth goal of his loan spell from Napoli after 24 minutes before Del Piero doubled Juve's advantage. Zlatan Ibrahimović pulled one back for Milan in the 82nd minute but Juve held on.
Salzburg were held 1-1 by Rapid Vienna in front of a 20,100 crowd, the Austrian Bundesliga's best of the season, when the visitors pounced on a late defensive error to wipe out Roman Waller's 12th-minute opener.
Red Bulls coach Huub Stevens admitted: “It is a very disappointing result for us, but in the second half we did not play football at all. That is the most worrying thing ... you can’t win like that.”