Cardiff thought they had taken the lead in the 18th minute when Bothroyd headed home another Matthews free-kick, but the linesman's flag had already gone up for offside.
Following a scrappy passage of play the game then exploded into life with a spell of four goals in six minutes at the end of the opening period.
Cardiff went in front in the 41st minute following a farcical mix-up in the United defence.
Bothroyd had the simple task of beating Bennett from four yards after Chris Morgan's clearance had struck Harper on the backside.
There was initial confusion as the linesman flagged for offside against Bothroyd, but referee Trevor Kettle correctly awarded the goal as the ball had reached the Cardiff striker via an opposition player.
United levelled almost immediately as Glen Little's cross was headed back towards his own keeper by Hudson, but fell invitingly short for Henderson to slot home.
The visitors regained the lead in the 45th minute, Whittingham making no mistake from the penalty spot after Henderson had hauled down Bothroyd.
Remarkably the Blades equalised again in the subsequent three minutes of stoppage time.
Marshall made a fine initial save to keep out Ched Evans' close-range header but the Scotland international was powerless to prevent Henderson heading home the rebound.
But Cardiff were back in front for a third time on the hour, as Matthews' long throw was flicked into the path of Whittingham who thumped home from close range.
United boss Blackwell brought on new signing Henri Camara as his side looked to rescue at least a point.
But although Kilgallon and Keith Treacy had chances to equalise, the Bluebirds remained a constant threat on the break and added a sensational fourth late on when Whittingham rounded off a slick passing move.
Harper did stab home an injury-time consolation for the Blades, before Quinn's late strike was chalked off to the disappointment of the disgruntled home support.
Sheffield United manager Kevin Blackwell:
"Things are tough at the moment, but the squad players that came in gave me a great shift and I can't knock them.
"It was a good performance and on another day it would have been enough to get us a point.
"It's tough when you are losing your experienced players and until we get them back it will be tough.
"But I think we deserved more than we got out of the game, that's for sure and the players showed terrific spirit to keep coming back."
Cardiff City manager Dave Jones: "The first half was a bit crazy... so I'm sure Kevin [Blades boss Blackwell] will be disappointed with his defending as much as I am with ours.
Cardiff boss praises Whittingham
"I just felt every time we got our noses in front we went and did something stupid.
"But our fourth goal today you won't see many better, our moving, our passing, our crispness and the finish.
"And well deserved for Whitts [Whittingham] to get his hat-trick... it was a tough game."
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