The Welsh side, whose play-off dreams ended in the final game of the season at Hillsborough in May, were in trouble in the fourth minute when Dutch winger Etienne Esajas firing Wednesday into the lead with a curling free-kick which hit the inside of the post on its ways past David Marshall.
Midfielder Chris Burke fired over from 15 yards before Cardiff escaped twice in the space of a minute, on-loan Derby striker Luke Varney hitting the woodwork with a a low strike and then heading narrowly over from Michael Gray's precise cross.
Cardiff were back on level terms in the 16th minute when Michael Chopra was brought down in the area by Lee Grant as the pair chased a loose ball. Peter Whittingham coolly dispatched the penalty, for his fourth goal of the season.
Anthony Gerrard headed over and Jay Bothroyd saw his fierce strike scooped up on the line by Grant as Cardiff grew in confidence but it was the Sheffield side who almost snatched the lead again, Esajas trying his luck with a strike from 30 yards as Marshall scrambled back to save.
Wednesday added a second three minutes after the re-start, the impressive Esajas pumping over a perfect cross as Varney stretched to steer his glancing header beyond Marshall.
The Sheffield side tightened their grip on the game, Esajas firing in a shot from 20 yards that was pushed away by the keeper before substitute Leon Clarke, on for Marcus Tudgay, finished a strong run with a vicious strike, the ball hitting a post and spinning wide of the target.
Cardiff were in further trouble in the 73rd minute when Ledley was sent off after picking up his second booking with Leon Clarke adding the third seven minutes from time as he slotted in an Esajas cross from close range.