Bravo dived full length to deny Robben another goal as Bayern turned on the style.
But City got the goal their first half efforts merited just before the break as sub Bernardo Silva – who had replaced Mahrez – curled home from the edge of the box.
Soon after the restart City were level as Phil Foden – who had impressed in the first half – fired in a low shot.
It was only parried by the Bayern keeper and Nmecha was on hand to slot in the rebound.
And the comeback was complete midway through the second half thanks to some nice work from sub Adrian Bernabe.
The former Barcelona teen showed some nifty footwork to tee up Bernardo to score his second of the game with a crisp strike.