Jimmy Floyd Hasselbaink flipped a pass to the impressive Peter Whittingham, who backheeled to Parry out on the right and the Wales international fired in a low shot that went across Paddy Kenny in the visitors goal and into the far corner of the net.
There were two changes in the Bluebirds line-up with Tony Capaldi and Gavin Rae replacing the Spurs-bound Chris Gunter and the suspended Steve Thompson.
Straight from the kick-off the Blades went on the attack and after just 20 seconds James Beattie was left unmarked in front of goal, but blasted the ball over the bar.
Parry was pushed into a forward position alongside Hasselbaink and he provided an outlet for the Bluebirds as they began to mount a few attacks.
A burst by Joe Ledley in the 14th minute was halted by a block from Chris Morgan and Hasselbaink's powerful free-kick struck a United defender before being cleared.
Beattie was then off-target again with a header from a Keith Gillespie corner.
After Cardiff had taken the lead they began to grow in confidence and Whittingham forced Kenny into a smart save from a 20-yard snapshot.
He then swung over another goalbound cross that Kenny pushed behind, before a blockbuster was pushed away by the overworked Blades keeper.
The visitors suffered a blow in the 58th minute when skipper Morgan limped off to be replaced by one-time City target Chris Lucketti.
Two minutes later United boss Bryan Robson went for broke by putting on Rob Hulse and Lee Hendrie in an effort to get back on level terms.
But it was Whittingham and Parry who went closest to adding to the score with dipping shots that just cleared the visitors' crossbar.
When Michael Tonge was upended just outside the area in the 86th minute it spelt danger for the Bluebirds, but Phil Bardsley's rasping drive zipped past the right-hand upright.
City still had chances to add to their score in the dying minutes with Whittingham and substitute Steve MacLean both going close.