The Bundesliga champions were trailing to Marco Reus’ 31st minute strike as Dortmund looked to finally kick-start their faltering campaign.
The Black and Yellows held out until the 72nd minute when Robert Lewandowski returned to haunt his former employers and Pep Guardiola’s side rubbed salt in the wounds when Arjen Robben scored from the spot five minutes from time to complete the turnaround and extend Bayern’s lead at the top of the table to four points.
Bayern return to domestic action next Saturday where they face Eintracht Frankfurt.
In Serie A, Roma fell to defeat for only the second time as they were beaten 2-0 by Napoli.
The Rome side fell behind after just three minutes when Gonzalo Higuain scored for Napoli and Jose Callejon added a second just five minutes from time to leave Roma three points adrift of leaders Juventus.
With a crucial Group E encounter with Bayern on Wednesday, the Romans need to rediscover their impressive early season form as they shape up to what looks like a straight fight for second with spot in the table with City
Roma face 12th-placed Torino next Sunday.
In Russia, former City midfielder Javi Garcia struck a blow to CSKA’s hopes of winning the Russian Premier League.
The Muscovites were at home to leaders Zenit St Petersburg knowing a win would put them within one point of the summit, but Garcia scored what proved to be the only goal of the game just seven minutes in – his third in just nine games – to leave CSKA trailing unbeaten Zenit by seven points.
With the Moscow derby against Dinamo coming next in the league, CSKA know they can ill-afford to lose much more ground on the leaders.