A brace from Luis Suarez within 30 minutes of the game proved too much for City, who were only able to grab a late consolation through Sergio Aguero.
Lionel Messi had a very good chance to make the score 3-1 after he managed to win a penalty in injury time, but his spot kicked was saved by Joe Hart.
The game started with James Milner testing Marc-André ter Stegen from a low free-kick after Aguero was brought down by Javier Mascherano just outside the box.
However, that was the only attacking threat that City could produce in the first half as the Barcelona juggernaut led by Messi, Suarez and Neymar started gaining momentum.
Martin Demichelis, who was sent off during City's last season's first leg defeat to Barcelona, proved to be a hero in the early stages of the game as he twice rescued his side, blocking an effort from Messi in the 12th minute before heading away a dangerous cross from Suarez a couple of minutes later.
However, the Argentine defender's efforts went in vain as Barcelona broke the deadlock in the 16th minute through Suarez. Messi whipped a cross into the box and the former Liverpool striker connected with a header. Although his header was straight at Vincent Kompany, the ball rebounded towards Suarez, who this time made no mistakes as he slotted the ball clinically from a tight angle.
City striker Dzeko got a rare chance in the 22nd minute, but his header, following a cross from Clichy was wide of the target.
Four minutes later, Hart made a brilliant save to thwart Suarez, who had managed to fire a low shot on goal following some good work from Neymar and Messi.
However, City were not able to contain Suarez for long as he soon netted his second goal of the night just before the half hour mark.
Messi, after outfoxing a number of City defenders with some brilliant dribbling, sent an excellent pass towards a completely unmarked Jordi Alba on the left wing. The defender in turn squared the ball towards Suarez, who raced ahead to slide the ball past Hart.
Barcelona threatened to further increase their lead in the closing stages of the first half, but City managed to prevent the Catalans from inflicting more damage, and the two sides went into the break with the scores reading 2-0 in the visitors favour.
City boss Manuel Pellegrini's half time pep talk seemed to have made some impression on his players as the hosts looked a little more positive after the break.
Dzeko got a very good chance to pull a goal back for his side in the 49th minute, but his header, from a corner, was wide off the target.
Moments later, an excellent cross from Kompany gave Dzeko another opportunity, but the Bosnian striker again failed to take advantage as his header was straight at Marc-Andre ter Stegen.
More chances followed for City as the match drifted towards the hour mark, but Aguero could not get his shot no target and Samir Nasri's had his effort blocked.
City's continued efforts soon paid dividends as they finally pulled a goal back in the 69th minute through Aguero, who showed great composure to avoid a challenge from Gerard Pique and lob the ball over Ter Stegen.
Just as the Citizens looked like they were going to make a comeback, Clichy received his marching orders after collecting his second yellow of the night following his foul on Dani Alves.
Finally Barcelona got a very good chance to restore their two goal cushion after Zabaleta was penalised for bringing down his compatriot Messi inside the box in the fourth minute of added time.
Messi stepped up and fired the penalty towards the bottom right corner, but an alert Hart managed to keep his effort out. The Argentine was quick to react to the rebound, but his header was way off the target.