The Bluebirds, aiming to capitalise on Derby County's draw against Bristol City by the same scoreline on Friday night, could not find a way through from some speculative attempts in the first half.
Wednesday were unlucky not to snatch all three points in the second period, creating two big chances for Lucas Joao which the striker failed to make the most of.
Cardiff had the better of the first-half chances and found the net through Kenneth Zohore, who expertly found a way past Joe Wildsmith from range but only after the whistle had already blown for an infringement.
Another of the Bluebirds' new recruits, Liverpool man Marko Grujic, was next to test the busy Wednesday stopper with a similar attempt that was heading for the bottom corner.
The Owls ended the opening 45 minutes on top, though, with Jordan Rhodes fluffing his lines from a headed chance in the box and Adam Reach blasting over a half-empty goal after the ball was parried into his path.
Wednesday took that momentum into the second half and should have opened the scoring when Joao was played through, but he dragged his shot wide of the post under pressure from covering defender Sol Bamba.
Joao had an even better chance minutes later, only to this time head straight at Neil Etheridge with his back-post header under little pressure.
Etheridge was alert in the final 15 minutes to pounce before Marco Matias could convert, which would prove to be the last opening of the evening.
SHEFFIELD WEDNESDAY (3-5-2): Wildsmith; Thorniley, Venancio, Pudil; Palmer, Jones, Reach, Wallace (Boyd 81'), Fox; Joao (Nuhiu 81'), Rhodes (Matias 72')
CARDIFF CITY (5-4-1): Etheridge; Manga, Morrison, Bamba; Richards, Ralls, Grujic (Paterson 78'), Bennett; Hoilett (Harris 83'); Wildschut (Mendez-Laing 71'), Zohore