New boss Paul Jewell's predecessor Roy Keane never managed that feat during 20 months in charge but Town looked a completely different animal as they played with confidence in contrast to the Blades who are still waiting for their first win under Micky Adams and are languishing in the drop zone.
Damien Delaney put talk over his future to one side as he broke the deadlock midway the first half by heading home a free-kick from home debutant Jimmy Bullard.
And it was another man linked with a move away from Portman Road - captain David Norris - who converted Delaney's cross shortly after the interval to leave himself one short of a 10-goal season haul for the first time in his career.
Tamas Priskin hit a post for Town while Grant Leadbitter saw his late penalty turned around the post by Steve Simonsen, but there was nothing the Blades stopper could do to deny highly-regarded youngster Connor Wickham a stunning virtuoso third in the 87th minute.
A miserable afternoon was made even worse for United as the visitors saw substitute Rob Kozluk and midfielder Liam Williamson sent off within a minute of each other in the closing stages.
Jewell named an unchanged 18 from Tuesday's 2-1 win at former employers Derby, while Blades counterpart Adams made two alterations to his starting line-up following the midweek home defeat to Leicester - debutant Neill Collins and forward Daniel Bogdanovic coming in.
It was the visitors who edged proceedings in the opening stages although they failed to create any clear-cut openings of note.
And, with Town firmly back in the game, the Portman Road faithful were brought to their feet with 29 minutes on the clock as Delaney headed home his third goal of the season.
Bullard saw his superb crossfield pass to Norris subsequently handled by Shane Lowry and, from the resulting free-kick out wide, floated over another great ball for the unmarked Delaney to nod past Simonsen.
The South Yorkshire outfit had failed to really test goalkeeper Marton Fulop as the half-time whistle blew, and within eight minutes of the restart they found themselves two goals down.
Delaney whipped over a cross from the left and Norris did extremely well at the far post to find enough space to send the ball home.
It was nearly three just minutes later as Priskin hit a post from 18 yards.
Adams introduced all three of his substitutes in a bid to change matters but they failed to have any real effect and it was left for Simonsen to prevent further misery as he denied Leadbitter from the spot in the 82nd minute.
Yet Wickham did add further insult shortly after as he picked up the ball on the halfway mark before beating a handful of black shirts and the United stopper.
And just when Adams thought his afternoon could not get any worse Kozluk saw red for violent conduct and Williamson talked himself into a second yellow card.