Tammy Abraham’s second goal in as many games was enough to secure City’s place in round two of the EFL Cup.
The loan signing from Chelsea followed up his equaliser against Wigan Athletic on the opening day of the league campaign with a low shot that found the bottom corner in the 27th minute at Adams Park.
The Sky Bet League Two hosts had their chances to force extra time, but Richard O’Donnell was in inspired form when called upon and a much-changed City side saw the job through.
Lee Johnson made a total of seven alterations to his side following the dramatic victory over the Latics three days ago.
Only O’Donnell, Aden Flint, Marlon Pack and Lee Tomlin survived the cull, as Adam Matthews, Derrick Williams, Scott Golbourne, Bobby Reid, Luke Freeman, Aaron Wilbraham and Abraham all came in.
City enjoyed some good early possession without testing emergency loan signing Cameron Dawson in the Wycombe goal.
Getting Abraham in behind the defence seemed to be Plan A, with both Flint and Tomlin sending the teenager on the run in the opening exchanges.
Reid and Pack both tried their luck from distance, with Dawson comfortably holding the Bristolian’s effort before seeing Pack’s shot sail narrowly wide.
The hosts included supersized striker Adebayo Akinfenwa in their ranks, who gave Matthews an uncomfortable moment when he outjumped the Welshman at the far post only for his header to deflect behind for what should have been a corner, had the touch been spotted by the officials.
But it was from a cross of their own that City went in front on 27 minutes. Former Wycombe loanee Golbourne picked up an advanced position down the left flank and found Abraham with a low ball that the Chelsea loanee controlled and finished with a low shot just inside the post – not the cleanest of strikes, but no less effective.
The fourth tier outfit still had reason to believe they could cause problems and should have drawn level nine minutes later.
Akinfenwa’s sheer physique kept the ball alive after it bounced around in the City box, laying it off for Sam Wood to stand up a cross to the back post that should have been buried by the onrushing Michael Harriman, who somehow headed over from six yards.
But the visitors still carried the greater threat and twice came close to doubling the lead in quick succession, potentially putting the tie to bed in the process.
The ever-dangerous Flint rose to meet Reid’s corner with a thumping header cleared to temporary safety from the goal-line, before Tomlin found Wilbraham, whose curling shot only just eluded the angle of post and bar.
Gareth Ainsworth, Wycombe manager and substitute for the night due to an injury crisis, had his players fired up for the second period and City were indebted to their goalkeeper three times in a minute.
First, skipper Matt Bloomfield escaped down the right and crossed low to Dayle Southwell, who looked certain to score only for O’Donnell to excel himself with a stunning point-blank save, before tipping Bloomfield’s low drive around the near post.
When the resulting corner was not properly cleared, Anthony Stewart tried his luck with a fierce strike again repelled by the City custodian.
Johnson used all three of his substitutions in one fell swoop midway through the second half, despite the possibility of extra time and penalties.
Matthews, Wilbraham and Abraham were the men sacrificed, with Mark Little, Joe Bryan and Arnold Garita – a Cameroonian striker making his City debut – the trio introduced.
Bryan’s first contribution was to whip in a free kick glanced goalwards by Flint but only into the grateful grasp of Dawson.
City seemed content to keep the possession as the clock ticked down into the final ten minutes, but would have to survive a late scare when O’Donnell again made an important stop before Akinfenwa tapped in the rebound only to be flagged offside.
Still Wycombe believed they could go the distance, but O’Donnell stuck out a leg to keep Akinfenwa at bay and City did what they had to do to be in with a chance of facing Premier League opposition in the second round.