Tammy Abraham came off the bench to score an extra-time winner and book City’s place in the EFL Cup third round.
Hosts Scunthorpe United were thoroughly outplayed by a slick visiting team in the first half in particular, but City only had Bobby Reid’s 35th-minute goal to show for their dominance.
Scunthorpe maintained their belief and found an unlikely route back into the tie on the hour mark when Josh Morris scored from the penalty spot.
But Abraham, who arrived shortly after the equaliser, ensured there would be no further spot-kicks with a ruthless finish on the turn seven minutes into extra time.
Lee Johnson made seven changes to his side – just as he did for the trip to Wycombe Wanderers in round one.
Mark Little, Derrick Williams, Marlon Pack, Josh Brownhill, Callum O’Dowda and Aaron Wilbraham were all recalled, but perhaps most notable was the inclusion of Frank Fielding, with the goalkeeper making his first appearance in seven months after an ankle injury.
Johnson would have been pleased with his team’s intensity in the early stages. City were popping the ball about quickly and with purpose, responding to the boss’ wish to see balls crossed into the box with greater urgency having fired two blanks against promotion favourites Norwich City and Newcastle United.
The busiest player on the pitch in the first 15 minutes was Scunthorpe goalkeeper Luke Daniels.
The former Manchester United trainee showed his agility to make a flying stop from Luke Freeman, who traded passes with Wilbraham and hit a thunderbolt towards the top corner from 20 yards.
From the resulting corner, Aden Flint’s downward header was clawed away by the keeper before the rebound fell kindly for Reid, but the Bristolian’s vicious shot knocked team-mate Brownhill clean off his feet and the hosts survived.
Reid was annoyed that his goalbound effort had not reached its intended target, but he used that frustration to good effect when he steamed into the box and cut the ball across goal to O’Dowda, whose firm sidefoot again brought out the best in Daniels.
City will have been wondering how they were not in front, but Little was called upon to prevent the opening goal coming completely against the run of play when his last-ditch tackle halted Morris in his tracks.
It would prove only a temporary form of respite for the Scunny defence. Another Pack corner caused problems when Daniels looked less convincing in keeping Flint at bay, before O’Dowda’s follow-up was cleared off the line and Pack’s 25-yarder was parried to safety.
City had been utterly dominant and finally got the goal their first-half performance merited ten minutes before the break.
There was an element of good fortune in the build-up when Scott Golbourne’s deflected pass opened up the pitch for Reid.
When he slipped it to his right, Brownhill looked set to score only to send a powerful shot against the near post. Just as City may have been feeling it was never going to go in, Reid collected the rebound, steadied himself and drilled a low shot into the net to finally beat Daniels.
The second half followed a similar pattern but for Fielding’s first notable save to keep out Kevin Van Veen after City allowed a high ball to bounce.
Otherwise it was more attack against defence. O’Dowda headed wide and Freeman too high from two very well-worked moves down the left flank, while Brownhill fired over from a free kick on the edge of the D.
But Johnson will be the first to say a 1-0 lead is a precarious one, and United were given a route back into the game on the hour when Williams was adjudged to have tripped Stephen Dawson as the captain charged towards the dead-ball line.
The Irishman was baffled by the decision and immediately cautioned, before Morris stepped up to send Fielding the wrong way.
Seven minutes later, the City head coach made the sort of decision that suggested he did not fancy the prospect of extra time.
Reid and Wilbraham were sacrificed to allow Lee Tomlin and Abraham to enter the fray, and the replacements instantly combined to good effect.
Tomlin’s through ball left Abraham with only Daniels to beat – or so he thought – as the striker’s clever dink was destined for the bottom corner only for Charlie Goode to intervene with a sliding clearance just in the nick of time.
City upped the pressure with every passing minute in a bid to get the job done without the need for an additional half-hour, but Scunthorpe were standing firm.
Tomlin became increasingly influential, shooting narrowly wide from 20 yards and looking to link up with Abraham at every opportunity.
There was to be one last chance in stoppage time, but the Chelsea loanee was forced wide and could only shoot against the legs of Daniels from Tomlin’s pass.
Abraham certainly looked the most likely and duly delivered the knockout punch seven minutes into extra time.
Little had defended well at right-back but it was his attacking exploits that paved the way for City to regain the lead, as he surged forward and hit an ambitious shot smartly controlled by Abraham, who turned and lashed the ball into the roof of the net in one clinical movement.
Johnson introduced Diego De Girolamo for his City debut shortly after, and the forward may have been among the penalty takers had Duane Holmes not inexplicably shot wide from Scott Wiseman’s cross with nine minutes left.