Campbell, a recent arrival from Sunderland, capitalised on a defensive mix-up to convert from six yards just two minutes after replacing Bo-Kyung Kim in the second half.
Malky Mackay's side have now dropped only two points in their last seven matches, but by no means had it all their own way at Elland Road and needed a fine late save from goalkeeper David Marshall from Tom Lees' header as they extended their unbeaten league run.
Two of Leeds' deadline-day signings, Stephen Warnock and Habib Habibou, were among the substitutes, but there was no place for the third, Steve Morison, currently sidelined with a thigh injury.
Cardiff also included a new signing, with Campbell starting on the bench, while both Craig Bellamy and defender Ben Turner returned to the starting line-up following illness.
Leeds picked up where they had left off in last Sunday's FA Cup win over Tottenham and looked the more likely side to open the scoring.
Striker Luke Varney pulled his early angled effort wide and Turner did well to block Ross McCormack's stinging drive following El-Hadji Diouf's short free-kick.
Cardiff had been restricted to Turner's header from Craig Conway's cross in the 27th minute and a long-range effort from the latter, while Barkley was denied at the other end with a thumping drive from outside the penalty area.
Leeds midfielder Michael Brown went close soon after the restart with a shot following Diouf's corner, but Cardiff went even closer in the 54th minute and should have scored when striker Tommy Smith steered the ball wide from only six yards.
Campbell made his Cardiff bow in the 61st minute when he replaced Kim and the former Sunderland forward broke the deadlock just minutes later.
Bellamy pounced on a Sam Byram mistake and Campbell was on hand to side-foot the ball home from six yards.
Byram's goalbound header was blocked by Mark Hudson and Marshall then saved brilliantly to keep out Lees' header in the 79th minute as Leeds pressed for the equaliser.