On-loan striker Neil Harris put Cardiff deservedly ahead on 41 minutes, but Graham Kavanagh was sent off a minute later after a wild lunge on Jon Harley.
The Blades piled on the pressure after the break and were level on 69 minutes when Andy Liddell slotted home after a clever pass from Michael Tonge.
Andy Gray snatched victory 11 minutes from time when he pounced on a loose ball in the six-yard box.
Cardiff City manager Lennie Lawrence:
"I've never been in such total control of a game here as we were in
the first half.
"There were three or four magnificent individual performances.
"The referee was an absolute disgrace. If [Peter Thorne's] goal had been at the other end, there's no doubt it wouldn't have been disallowed.
"He only got one thing right and that was the sending off."
Sheff Utd: Bennett, Geary (Liddell 45), Harley, Morgan, Bromby,
Cullip, Jagielka, Quinn (Thirlwell 88), Tonge, Gray,
Shaw (Cadamarteri 45).
Subs Not Used: Wright, Beckett.
Booked: Geary, Cullip.
Goals: Liddell 69, Gray 79.
Cardiff: Warner, Williams, Collins, Gabbidon, Barker, Kavanagh,
Boland, Ledley (Parry 80), Harris, Jerome (McAnuff 45), Thorne.
Subs Not Used: Alexander, Vidmar, Bullock.
Sent Off: Kavanagh (42).
Booked: Barker, Gabbidon, Harris.
Goals: Harris 41.
Ref: A Marriner (W Midlands).