Raheem Sterling and Gabriel Jesus got on the scoresheet, while Ryan Ledson added an own-goal in the first half. The second half saw plenty more chances, but no more goals.
Preston had already survived two rounds, while City played their first match in this season's competition.
City made several changes to their starting XI but still fielded several top players, including Bernardo Silva, Jesus and Sterling. It was the latter who looked liveliest early, and he had a weak penalty shout turned down after five minutes.
Preston more than held their own during the first 15 minutes, and chances were few. Sterling drew a fine save from goalkeeper Connor Ripley, who had little else to do until he conceded the opener.
It was Sterling once again who forced the action with a lovely run, before his deflected shot beat Ripley. Sports writer Ian Cheeseman thought it was a lovely goal:
Jesus thought he had doubled the lead minutes later after what appeared a great feed from David Silva, but the flag was raised for offside immediately.
The Brazilian would get his goal after 35 minutes, however, when Sterling picked him out and he produced a fine finish through Ripley's legs:
BBC 5 Live Sport @5liveSport
GOAL - Jesus 'Wonderful football. Sterling with a wonderful pass. Jesus drills the ball from 10 yards out and the speed of the ball means there was nothing the keeper could do! - Owen Coyle @pnefc 0-2 @ManCity 🎧 Listen live 👇 📲⚽️ https://t.co/0kUniX6SeW #bbcfootball #EFLCup https://t.co/iobv447HZU
And things got even worse for the hosts before half-time. Ledson tried to block a Silva cross with a slide, but accidentally put the ball past his own goalkeeper for City's third goal.
The first chance of the second half fell to Phil Foden, who just couldn't get his shot off fast enough and saw his effort blocked.
Jesus also went close after a good cross from Angelino, but he couldn't keep his header on target, while Eric Garcia somehow missed an open net minutes later. Preston also had their chances, with Josh Harrop striking the post.
Foden continued to threaten and struck the woodwork as well, finding the crossbar with a lovely attempt.
The pace of the contest dropped as the half wore on, with City focused on the final whistle and Preston powerless to force the action. Ripley had to make two more saves from Jesus in the last 10 minutes, denying the Brazilian another deserved goal.