The Blades created too few chances in a game which they had keeper Paddy Kenny to thank as City battered the visitors defence - in the end all the difference was Paul Parry's low strike after 30 minutes.
Striker Jimmy Floyd Hasselbaink dinked in a pass to Peter Whittingham who back heeled to Parry on the right as he fired in a stunning low shot past keeper Paddy Kenny.
Prior to the match Bluebirds boss Dave Jones made two changes with Tony Capaldi and Gavin Rae replacing Chris Gunter and Steve Thompson (suspended).
Despite their poor performance in the Welsh capital the Blades almost went ahead inside 20 seconds; James Beattie was unmarked and in an onside position in front of goal - but at the given opportunity blasted the ball over the bar.
In 14th minute Joe Ledley found himself haltered by Chris Morgan and Hasselbaink hit the wall before being cleared to safety. Top scorer Beattie then headed over Keith Gillespie's corner.
Cardiff City then took the lead when Parry's strike proved unstoppable for Kenny as City looked confident with Whittingham forcing the keeper into a great save from 20 yards.
The Blades hit a blow in 58th minute when skipper Chris Morgan was forced to leave the field with an injured leg, Chris Lucketti took his place.
Two minutes later Bryan Robson put all his eggs in one basket and threw on Rob Hulse and Lee Hendrie in an attempt to get back into the game - it failed.
Whittingham and Parry went closest for City with there dipping shots and in 86th minute Michael Tonge was mugged outside the area with Phil Bardsley's rasping drive zipping past the right post.