A deadly three-goal second-half strike gave Neil Warnock's Premiership hopefuls a richly deserved win over their Yorkshire rivals.
Midfielder Michael Brown grabbed two and livewire Peter Ndlovu added another to claim the points.
United, already assured of a play-off spot, turned on the style but wasted a string of chances as they forced City onto the back foot early on.
Carl Asaba smashed a fifth minute effort over the top but Bradford, who have survived the drop, had an early opportunity when United keeper Paddy Kenny produced an impressive stop to deny Danny Forrest.
But a stinging 30-yard effort from Michael Tonge warmed the hands of Aidan Davison as United looked for an opener.
Ndlovu was among the guilty Blades players as the chances came his way. A smart one-two with Brown took Ndlovu into the area but his shot was parried by Davison.
Asaba should have given the home side the lead ten minutes before half time but ex-United defender Gus Uhlenbeek raced in to clear with Davison beaten.
And midfielder Brown was off target with another long-range effort just before the break.
After the restart Ndlovu was high with a long-range effort before Dean Windass beat the keeper with a super shot that came back off the bar.
But on the hour Brown struck with the sweetest of shots to claim his 19th goal of the season.
A link up with Windass opened up City for Brown and he lashed a blistering effort from 25 yards to edge the home side in front.
And three minutes later Ndlovu's persistence paid off as he killed off the contest with United's second.
The pacy frontman burst into the box and stabbed a shot goalwards from close in. Davison dropped smartly to block the effort but he could only parry the shot and it sprang up and Ndlovu stooped to head the rebound over the stricken keeper.
And when Mark Bower gave away a 78th minute penalty with a shove on Paul Peschisolido, Brown hit his 20th of the season from the spot.