Hat-trick hero Peter Ndlovu helped settle an eight-goal thriller at Bramall Lane as the Blades preserved their unbeaten home record.
Cardiff contributed in fine style to a feast of spectacular football after this clash had been delayed 10 minutes due to crowd congestion.
Welsh striker Robert Earnshaw fired his 10th and 11th goals of the season, big strike partner Peter Thorne turned in a towering display and Cardiff midfielder Richard Langley capped a fine afternoon with a thundering 30-yard free-kick.
But it was not enough to deny Neil Warnock's side all three points thanks to Michael Tonge's superb free-kick, three goals - a wonder strike and two penalties - from Zimbabwean international Ndlovu and summer signing Jack Lester's decisive late volley.
Cardiff appeared to have benefited from an extra 10 minutes in the dressing room, Thorne firing in a goalbound shot from 30 yards inside 90 seconds that Blades keeper Paul Gerrard held.
Minutes later the on-loan Everton stopper was further extended, this time hurling himself to deny the in-form Graham Kavanagh by tipping his shot around his post.
Paul Peschisolido responded for the home side, but his long-range effort whistled over the crossbar before Mike Whitlow blocked another 20-yarder from Cardiff's Langley as the visitors shaded the early exchanges.
Ndlovu and Phil Jagielka both fired wide as the Blades tried to muscle their way into the match with striker Ashley Ward booked for his challenge on Chris Barker.
But Jagielka did well to block another rocket from Langley as Cardiff continued to take the game to the Yorkshiremen, while Jon Harley earned the second yellow card for his reluctance to retreat 10 yards after fouling Earnshaw on the edge of the penalty area.
England Under-21 international defender Jagielka then threw himself at another effort from Thorne and Peschisolido blazed over again as half-time beckoned.
Cardiff were first to the trigger again at the start of the second period. In a carbon-copy of the first half, Thorne let fly before everyone had taken their seats and this time Gerrard could only parry his 20-yarder before Earnshaw pounced to despatch the rebound.
But Cardiff's lead was short-lived. Within six minutes Langley brought down Harley within range and Tonge stepped up to curl his 25-yard free-kick beyond Neil Alexander for a spectacular equaliser.
Ndlovu's goal bound effort was then blocked by Rhys Weston, but the Zimbabwean was not to be denied his fifth goal in as many matches when out of the blue he fired the Blades ahead with a stunning shot from 35 yards, but back came Cardiff with a classic one-two.
Thorne headed the ball down into Earnshaw's path and the diminutive striker lashed home his 11th goal of the season low into the corner from the edge of the area.
Alexander then saved brilliantly from another Tongue free-kick before Cardiff regained the lead, Nick Montgomery penalised for handball 30 yards out and Langley firing spectacularly home.
But it takes more than the odd goal to knock the Blades out of their stride and Warnock's boys were level again when Ndlovu fired home from the penalty spot after Chris Barker had handled Montgomery's cross.
And, in a frantic finale, Lester raced onto fellow substitute Wayne Allison's header to volley home the winner from the edge of the area before Ndlovu converted his second spot kick after Willie Boland upended Tonge in the last minute.