Shaun Wright-Phillips rattled in the opener after it took a full-strength Blues 50 minutes to transfer their quality to the scoreline against a passionate young Palace outfit.
And Carlos Tevez, the striker who loomed large in Sheffield United’s bitter, disputed relegation under Neil Warnock, later headed home his first goal since joining City this summer.
Battling Palace, for all their efforts in a banana-skin tie, could not succeed where Blackburn, Barcelona and Wolves have failed this season to end Shay Given’s spotless clean-sheet record.
But Mark Hughes, mindful of last season’s dismal Carling Cup exit at Brighton, knows he took the right decision in loading his side with as many of his big-hitters as he could assemble.
There could hardly have been a greater contrast when the sides ran out - Palace, raw and inexperienced with manager Warnock blocked from any signings, against a mighty City line-up.
Hughes crammed all his fit big guns into the side, with new centre-half Joleon Lescott stepping in for Richard Dunne - in talks at Aston Villa - for the only change to Saturday’s winners.
But if Palace were totally eclipsed in the star-quality department, they were not lacking in sweat and commitment, and they refused to allow the Blues even a moment’s peace to settle.
Clint Hill powered a far-post header from a free kick straight at Given and Micah Richards picked up an early yellow card for clattering Victor Moses in a hectic first ten minutes.
Moses forced a fine save at full stretch from Given as Palace pressed, knowing they were vulnerable at the back to City’s pace when the Blues had the opportunity to pass the ball.
The eager Robinho should have put City ahead on just such an occasion, but was flagged offside even though he was in his own half to set off on what would surely have been a decisive run.
Even so, City were living dangerously, and Freddie Sears, on loan from West Ham, slipped the offside trap after 23 minutes only for Given, angle perfect, to stop the shot with his chest.
Hughes’ side cut through the Palace defence with incisive first-time passes when they got the chance soon after, but the offside flag denied Robinho once more, this time correctly.
Palace were reminded of the task they faced when City’s attack launched a mini-blitz as half time approached only to find Julian Speroni taking inspiration from opposite number Given.
First Emmanuel Adebayor’s languid dummy on the edge of the box gave the former Arsenal striker the chance to lash in a great shot that the goalkeeper did so well to parry over the bar.
Then a couple of minutes later Stevie Ireland effected a brilliant one-two with Carlos Tevez only for the little Argentine to be thwarted by a brave save from his fellow countryman.
It was a strong signal to the Championship side that City’s quality could undo them in a moment, and so it proved as the second half got underway with Palace full of hope.
Robinho and Ireland dealt the raking passes that took out the Palace defence and allowed Wright-Phillips to take one touch then smash a powerful shot beyond Speroni’s reach.
Once ahead in 50 minutes, City cast aside any inhibitions and were only denied instant additions by Speroni’s great save from Adebayor and the crossbar when SWP threatened again.
City’s superior quality and movement seemed certain to tell again before the end, but the clinching second goal eventually came from a corner - one of the Blues’ failings last season.
New boy Lescott made a run to the near post that took two defenders with him, and Tevez stepped off marker Shaun Derry to head neatly and comfortably past Speroni after 70 minutes.
Any glimmer of a famous comeback for Palace was extinguished when Derry sidefooted a decent opening straight at Given then the referee refused two late desperate shouts for a penalty.
