Whittingham himself had chances to score either side of half time and Joe Ledley also kept visiting keeper Paddy Kenny busy.
Michael Tonge had an effort late on for the Blades from a free-kick, but the visitors rarely threatened.
Sheffield United manager Bryan Robson:
"I thought we started well but we missed a few chances and James Beattie should have put us in front in our first attack.
"You cannot afford to miss chances like that at this level. Once Cardiff went ahead they defended very well to keep us out and our performance particularly in the second half became very scrappy.
"We have put teams under pressure in the past after going behind but Cardiff were excellent in defence and they have some very good players."
Cardiff: Schmeichel, McNaughton, Loovens, Johnson, Capaldi, McPhail, Ledley, Whittingham (Purse 90), Rae, Parry, Hasselbaink (MacLean 80).
Subs Not Used: Oakes, Blake, Ramsey.
Booked: Johnson.
Goals: Parry 30.
Sheff Utd: Kenny, Bardsley, Kilgallon, Morgan (Lucketti 58), Naysmith, Carney (Hendrie 60), Montgomery, Tonge, Gillespie, Sharp (Hulse 60), Beattie.
Subs Not Used: Stead, Armstrong.
Booked: Tonge.
Att: 12,869
Ref: Keith Stroud (Hampshire).
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