Wolves took the lead in the second minute through Matt Doherty after an error from Bluebirds keeper Ben Amos.
But goals from Matt Connolly and Pilkington completed a stunning second-half turnaround to earn Cardiff’s first win in seven games and they are now three points above the drop zone.
Doherty was allowed time and space to power the opener past Amos, who pushed the full-back’s goal-bound effort into his own net.
It was Doherty’s second goal in as many games after netting in Wolves’ dramatic 4-4 draw against Fulham on Saturday.
Cardiff’s response to going a goal down was good, and their first real opportunity came through Sean Morrison after he headed over a Whittingham free-kick.
Another chance arose for the goal-shy home side after an Aron Gunnarsson long throw found Kieran Richardson, who blasted over from close range.
Richardson was making his first start since signing on a free transfer two months ago, but the veteran utility man did not have an impact on the game and was hooked off at the break.
It was all Cardiff as the first half drew to a close and they should have equalised when Richardson found Lex Immers, who somehow failed to connect with the lofted cross.
The home side were booed off at half-time and Bluebirds boss Neil Warnock made a double substitution for the second period, bringing on Craig Noone and Kenneth Zohore for Immers and Richardson.
And the pair made an immediate impact after Wolves’ third-choice keeper Harry Burgoyne excellently tipped Noone’s effort away from goal and Zohore then went close shortly after as his scissor kick just cleared the bar.
Cardiff’s breakthrough came when Whittingham’s corner was emphatically met by Connolly to bring Warnock’s men level in the 68th minute.
And shortly after the equaliser, Amos made amends for his earlier clanger when he superbly denied George Saville from point-blank range.
His save would prove invaluable when Zohore teed up Pilkington, who fired the ball past Burgoyne with four minutes remaining.
Lambert’s men paid the price for sitting back after taking an early lead and trying to play on the break in the second half.
But it was Cardiff’s constant pressure that prevailed to give Warnock a vital win heading into a run of winnable games over Christmas.