Sky Bet League One side Wycombe snatched a shock 22nd-minute lead through Brandon Hanlan but that was a distant memory by the final whistle, with Riyad Mahrez scoring twice alongside strikes from Kevin De Bruyne, Phil Foden and Ferran Torres to banish some frustrations from Saturday's 0-0 draw with Southampton.
Guardiola had promised to give youngsters their chance as injuries hit ahead of Saturday's Premier League trip to Chelsea, but though he was true to his word there was a clear imbalance in the side he fielded to begin the pursuit of a fifth straight League Cup.
Five teenagers - Conrad Egan-Riley, Finley Burns, Luke Mbete, Josh Wilson-Ebrand and Romeo Lavia - started, but all in defensive roles, while captain De Bruyne led a powerful attacking unit also comprising Foden, Mahrez, Torres, and Raheem Sterling.
The early signs were promising but there was plenty of rust too - Sterling, Foden and Torres were all guilty of taking too long when finding space in the box.
At the other end, Wycombe's veteran powerhouse Adebayo Akinfenwa looked ready to feast on City's young back four - none of them born when the 39-year-old was collecting his first honours in Lithuanian football.
The threat from set-pieces was obvious, and Wycombe took the lead when City failed to deal with a 22nd-minute corner.
American goalkeeper Zack Steffen - fit to start after recovering from Covid-19 - could only punch the ball as far as Sulley Kaikai, whose shot was deflected, spinning into the path of Ryan Tafazolli who squared it for Hanlan to side-foot home.
City were level seven minutes later. It started with superb work from Foden in midfield, side-stepping two before hitting a defence-splitting pass to De Bruyne on the left, with the Belgian calmly passing the ball into the far corner of the net.
Guardiola's side were getting into a groove as the manager enthusiastically applauded the efforts of his younger players pushing forward. Sterling and then Mahrez both bent shots on to posts before two quick goals put them in control before the break.
Mahrez got the first with a crisp finish, but much of the credit belonged to the young Wilson-Ebrand, who teased Wycombe full-back Jason McCarthy before pulling an inviting ball back to the penalty spot.
And moments later Foden underlined City's superior class, collecting a short corner and unleashing a thunderbolt from 25 yards, leaving David Stockdale unable to do more than help the ball in.
City's teenagers might have been grateful to see Akinfenwa withdrawn just after the hour, replaced by Sam Vokes, but Wycombe could still threaten and Steffen did well to close down and block Jordan Obita's shot.
But City effectively killed the tie off moments later as Torres capped a sweeping move, side-footing home as Foden sent a low ball across goal.
It was the Spaniard's last touch - with Guardiola already preparing a double substitution which saw him replaced by Palmer while another teenager, Jason McAtee, became the sixth debutant on the night in place of Wilson-Esbrand.
The fifth goal came from familiar sources with De Bruyne releasing Sterling to pull the ball back for Mahrez to bag his second of the night.
But the biggest cheer came in the 89th minute as Palmer got City fans off their feet. The 19-year-old picked up the ball inside his own half and ran at the tiring Wycombe defence before curling a shot into the bottom left-hand corner of the net - the highlight of an encouraging night for City's future.