Aguero raced through to slot past Manuel Neuer in the 85th and 91st minutes to snatch a stunning win, the Argentine having given City a 21st minute lead with a penalty after Bayern’s Mehdi Benatia was shown a red card for bringing him down.
Two goals in quick succession from the away side gave Pep Guardiola’s men an unlikely 1-2 interval lead, a scoreline that left City with a mountain to climb. Xabi Alonso and Robert Lewandowski had struck within five minutes of each other shortly before halftime to put the visitors in front at the break.
But just as it looked like the German outfit would see out the victory a few errors crept into their game and City took full advantage thanks to two excellent finishes from Aguero.
City are level on five points with CSKA Moscow and AS Roma, who earlier drew 1-1, and know if they win in Rome and the Russians fail to beat Bayern in the final round of Group E matches they will qualify for the last 16.