Sergio Aguero struck in stoppage time to secure a 2-1 advantage for the Premier League leaders after the underdogs threatened an upset at the Etihad Stadium.
The Championship side went ahead on the stroke of half-time though Bobby Reid’s penalty before Kevin De Bruyne capped off a fine move to equalise 10 minutes after the interval.
It looked like the tie would be heading to Bristol all-square but Aguero came off the bench to nod in a stoppage-time winner.
City still have it all to do, but Guardiola says they will not be heading to Ashton Gate just defend their lead.
“They are a fantastic team,” Guardiola revealed after the game. “That’s why they knocked out four Premier League teams. Without that they will not be in the semi-final.
“They can play, long balls, they are fast, they know exactly what they have to do. Of course we will attack in Bristol and we’re going to try and win.”
Tottenham Hotspur midfielder Dele Alli has admitted he does not welcome allegations against him of diving, although he claims to be undistracted by them.
Karen Brady 'Let me be frank. The Board takes full responsibility for our predicament'
Despite being three wins away from FA Cup glory, Mauricio Pochettino has admitted the achievement would pale in comparison to a Premier League title.
Under-fire Baggies coach Alan Pardew has demanded his senior players improve their performance and help the troubled bottom of the table English Premier League side get a win in Saturday's fixture against Bournemouth.
Liverpool will want to banish the recent memory of losing to fierce rivals Manchester United with a big win against Watford at Anfield on Saturday evening.
Struggling Stoke City manager Paul Lambert is determined to keep his side in the Premier League ahead of Saturday's crucial clash against Everton at the Bet365 Stadium in Staffordshire.