Jason Price's sensational strike handed Hull an early advantage before United hit back strongly through goals from Paul Ifill, Danny Webber and Chris Armstrong.
The win restored the Blades' 11-point advantage over third-placed Leeds while the quality of their all-round play suggested they are a Premiership force in waiting.
Their superior class ultimately told in the sides' first meeting for almost 16 years - but Peter Taylor's men played their part in an enthralling opening half.
United fashioned the first goalscoring opportunity when David Unsworth's second-minute corner from the left flank found Neil Shipperley lurking at the far post.
The striker steadied himself before hitting a powerful effort which flew over the bar, though his team-mate Michael Tonge came much closer 10 minutes later.
Hull failed to clear a long throw and Tonge's 10-yard volley required goalkeeper Boaz Myhill to make a fine reflex save.
However, Nick Barmby, back in the side as skipper after being dropped from the starting line-up for the 2-0 defeat at Leeds on New Year's Eve, soon emerged as a key influence for Hull.
He was at his impudent best after 20 minutes, collecting a flick from Billy Paynter and hitting a delightful lobbed effort which looked to have beaten Paddy Kenny.
But the United keeper arched himself backwards to make an excellent finger-tip save over the bar.
Paddy was powerless to prevent Hull from taking the lead three minutes later, though, as midfielder Price strode forward on to the edge of the box and curled a brilliant left-foot shot into the top corner.
The Tigers were buoyant and when Price threatened to escape from United's last line of defence after 26 minutes, he was hauled down by Blades defender Unsworth, who escaped with a yellow card.
The Blades weathered the storm, however, and hit back shortly after the half hour mark to claim a precious equaliser. Ifill collected the ball on the edge of the box and hit a left-foot effort which fortuitously deflected off Hull left-back Andy Dawson and over Myhill.
Hull continued to impress - defender Leon Cort fired against the post - but they were stung on the stroke of half-time when United forged ahead in controversial circumstances.
Price looked to have been fouled by Unsworth deep in the visitors' territory, but referee Mike Thorpe saw no wrongdoing and waved play on.
Unsworth promptly punted ball upfield to Webber, who raced into Hull's 18-yard box and buried a low shot past Myhill into the far corner for his seventh goal of the season.
United almost claimed their third of the night shortly after the break when Phil Jagielka crashed a shot against the bar, but Armstrong's tidy 52nd-minute finish from Webber's pass was the final nail in the Tigers' coffin.
Hull continued to battle bravely but United remained a threat on the counter-attack and could ultimately have won by a greater margin.