The Bundesliga club took full advantage of a shambolic defensive display by the visitors in the first half.
Serbian midfielder Filip Kostic struck after 14 minutes and further goals followed from midfielder Daniel Didavi after 30 and fellow German striker Daniel Ginczek who netted twice in the 35th and 36th.
A week before the start of the Premier League season, City manager Manuel Pellegrini selected a strong, if adventurous, lineup in which 20-year-old George Evans was chosen to hold the midfield behind five forwards.
Ivory Coast midfielder Yaya Toure and City's South American players did not feature at all.
Pellegrini withdrew captain Vincent Kompany at halftime, replacing him with fellow Belgian Jason Denayer in a reshuffle that saw Ivory Coast striker Wilfried Bony replaced by 18-year-old Nigerian striker Kelechi Iheanacho.
Argentine Bruno Zuculini also came on for Evans and City hit back with two goals in the final eight minutes.
The lively Iheanacho grabbed the first and late substitute Edin Dzeko notched the second, the Bosnian target man converting from close range in what may be his final appearance before joining AS Roma.
According to media reports, the two clubs have agreed a fee of 14 million pounds ($21.88 million) for Dzeko.
(Reporting by Tim Collings, editing by Tony Jimenez)
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