Blackpool were forced to play all of 87 minutes with a numerical disadvantage after referee Andre Marriner showed goalkeeper Paul Rachubka a straight red card for bringing down Shefk Kuqi on his way to goal.
But Campell's cool penalty ensured all three points for the Seasiders as Palace slumped to their fourth Championship defeat on the spin.
The resulting free-kick from Rachubka's sending-off saw John Oster go agonisingly close to making it a double whammy for Palace but his curling effort smacked the top of the bar.
Replacement goalkeeper Matt Gilks made good saves from Kuqi on two occasions to keep the Seasiders on level terms.
And Tony Parkes' side, inspired by heroic central defensive displays from Shaun Barker and Ian Evatt, took a quite unthinkable lead four minutes before the break after Oster tripped Roy O'Donovan just inside the box leaving Campbell to slot home the spot-kick.
Neil Warnock responded to his side's disappointing opening period by making a double substitution, with new signing from Arsenal Rui Fonte and James Scowcroft replacing Nick Carle and Alan Lee.
But the home side continued to toil against the ten men and Campbell missed a glorious chance to double Blackpool's lead but could only flash his angled drive from ten yards across the face of goal in the 62nd minute.
If Blackpool were expecting a second-half Palace onslaught then they would have been pleasantly surprised as the home side failed to create any clear-cut chances despite their numerical advantage.
Fonte saw a tame effort blocked inches from goal in the dying seconds, but in reality Blackpool comfortably held on for a resilient victory.