Strikers Nicky Maynard and Rudy Gestede, who had earlier come on for the injured Andreas Cornelius on the stroke of half-time, struck to ensure the 2012 finalist's passage.
James Beattie's Accrington had given a good account of themselves before the 81 places between the two in the Football League pyramid became apparent.
The visitors were entirely unrecognisable from the XI which stunned Manchester City at the Cardiff City Stadium three days ago. And there was little of evidence of the high energy levels which were the hallmark of Sunday's win.
Of more concern to boss Malky Mackay was an ankle injury to debutant Cornelius, a £7.5million buy from FC Copenhagen, as he was withdrawn at the end of a 45 minutes to forget.
His misfortune may provide opportunities for Maynard and Gestede in the coming weeks and they made their mark early in the second half.
Maynard broke the deadlock just after the hour with a self-made goal before Gestede also found the net with a sweet first-time shot.
None of the Bluebirds team who started Sunday's 3-2 victory over City, their
first in the top flight for over 50 years, were involved in Accrington.
But striker Cornelius, who broke the club's transfer record earlier this summer
prior to Gary Medel's arrival, made his first start.
Beattie did not have such an embarrassment of riches at his disposal and, due
to injuries and suspensions, two debutant teenagers were on the Stanley bench
while goalkeeper Marcus Bettinelli, acquired from Fulham on loan just hours
earlier, was drafted straight into the line-up.
He had a trouble-free opening 20 minutes and it was his opposite number Joe
Lewis who would be tested first as he parried away Kal Naismith's stab at goal.
The south Welsh side had stunned City with a pair of goals from corners and it
was nearly that very method which did for Stanley. When the first delivery was
not dealt with properly the ball came back in and Mark Hudson's header was
nodded off the line by captain Luke Joyce.
Yet Beattie's men were acquitting themselves well with Cornelius largely
starved of service.
Indeed his frustrating first start in English football lasted just 45 minutes
as he injured his ankle in a sliding challenge from Tom Aldred. Cornelius, who
sustained a similar injury in pre-season, immediately beat the turf with his
fists prior to be taken off on a stretcher.
It was to be the last notable action of a first half in which there was very
little to separate the two teams.
Accrington restarted with plenty of purpose; less than a minute into the second period a long throw broke to Michael Richardson, whose effort was diverted just over via Kevin McNaughton's block.
It provided a wake-up call for Cardiff.
Jordon Mutch fired wide before Stanley were again indebted to a goal-line
clearance. Maynard sprung the offside trap and rounded Bettinelli and, although he was pushed wide, he turned the ball across for Tommy Smith to smash towards goal where full-back Luke Clark denied him.
Yet Cardiff kept the pressure on and soon hit their opponents with two quick
Maynard collected a pass from Smith and flicked the ball around the corner to
give himself the time and space to roll into the far corner.
It was a glimpse of the gulf in class and Gestede soon provided another 85
Mutch's low cross found the substitute at the back post and, first time, he
rifled the ball home with the outside of his boot.
It triggered a raft of changes from both sides with Beattie introducing
16-year-old Connor Mahoney, who was a bright spot, while Clark and Shay McCartan almost gave Stanley a consolation only to skew off target.