Bobby Reid stunned the Etihad with a penalty two minutes before half-time. Reid’s glory was short-lived after Kevin De Bruyne equalised for the Premier League leaders.
But after then, the visitors were worthy of taking a 1-1 draw back to Ashton Gate. But deep into injury time, Bernardo Silva clipped a ball to the edge of the six-yard box and substitute Aguero headed home.
Having dispatched Manchester United in the previous round, Lee Johnson’s men were on course for a famous double.
Pep Guardiola made four changes to the team that beat Burnley in the FA Cup on Saturday, which was the closest he has come to naming a weakened side, with rare starts for Yaya Toure, Oleksandr Zinchenko, Eliaquim Mangala and Claudio Bravo.
But the hosts were a team rammed with proven internationals and despite the Robins dumping out four top-flight teams to get this far, this was a classic David and Goliath affair.