The Bluebirds twice threw away the lead in a breathtaking conclusion to the first half, but Whittingham, who now has nine goals in his last six games, put them in front again on the hour mark before adding a wonderful fourth in the closing stages.
James Harper grabbed an injury-time consolation for the Blades and there was further drama when Stephen Quinn saw a late equaliser ruled out for offside.
The result means United have now lost three successive league games for the first time since April 2007, while their unbeaten home record has also come to an end.
Jay Bothroyd opened the scoring for the visitors in the 41st minute after Chris Morgan's attempted clearance rebounded off Harper but Darius Henderson pulled United level within two minutes.
Cardiff then went ahead again in the 45th minute, Whittingham drilling home a penalty after Henderson had hauled down Bothroyd in the box.
However the Blades showed great character to draw level again in first-half stoppage time, Henderson heading his second goal of the game.
Kevin Blackwell made four changes to the United side that lost 3-0 at Blackpool in midweek.
Ian Bennett replaced Mark Bunn in goal and there were also recalls for Ched Evans, Glen Little and Keith Treacy.
Cardiff boss Dave Jones opted to name an unchanged starting XI after his side's 2-0 victory over Coventry on Tuesday.
The Bluebirds came close in the first minute. Adam Matthews' lofted free-kick was headed out to Anthony Gerrard but the centre-half drilled his shot wide from the edge of the area.
United had an opportunity of their own soon after, but Gerrard was on hand to clear Morgan's goal-bound strike after goalkeeper David Marshall had flapped at Kyle Walker's cross.
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 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 Little's cross hit Mark Hudson and fell invitingly for Henderson to slot home. But the visitors regained the lead in the 45th minute, Whittingham making no mistake from the penalty spot after Henderson had hauled down Bothroyd.
Remarkably, United equalised again in the subsequent three minutes of stoppage time. Marshall made a fine initial save to keep out Evans' close-range header but he was powerless to prevent Henderson heading home the rebound.
Matt Kilgallon volleyed over for the Blades nine minutes after the interval following Henderson's intelligent knock-down. 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 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.