Two goals inside the opening seven minutes from Ched Evans and Richard Cresswell looked to have put the Blades on course for their first win under the management of Micky Adams.
The visitors were unable to make the most of a dominant display in the first half hour and on-loan Nottingham Forest striker Joe Garner scored twice before the break to bring Scunthorpe level before Lee Miller headed his first goal for the club eight minutes into the second half.
The visitors were unable to find an equaliser and suffered further anguish in the closing stages as Shane Lowry was sent off for a foul on Garner.
Scunthorpe leapfrog their opponents in the table as a result of their triumph, but Adams will wonder how his side managed to throw away a much-needed three points.
Ian Baraclough, the Iron manager, named the same starting XI that drew at home to Derby on Saturday.
The Iron wasted a great chance to open the scoring in the fourth minute. Mark Duffy’s cross found Garner completely umarked 10 yards out, but the forward failed to keep his header down.
The Blades then grabbed two goals in quick succession. Evans opened the scoring in the sixth minute with a drilled left-footed shot from 15 yards after Scunthorpe had failed to clear a right-wing cross.
The lead was then doubled in comical fashion as Cresswell charged down a clearance from home goalkeeper Josh Lillis and watched on as the ball rolled into an empty net.
A shellshocked Iron struggled to respond and Evans spurned a good chance to add a third following good work from Bjorn Helge Riise down the right.
Riise then struck the bar from 25 yards with Lillis rooted to the spot, but the hosts were handed a lifeline eight minutes before the break as Garner thumped home a penalty after he had been bundled over inside the box by Neill Collins.
Evans tested Lillis and saw another effort drift narrowly wide before Scunthorpe dramatically pulled level in the 44th minute.
A deep free-kick from the right was headed across goal by Michael Nelson and Garner was on hand to tap home from close range.
Worse was to follow for the Blades as they were undone by another set-piece eight minutes into the second half.
Duffy floated over another dangerous ball from the right and Miller rose above his marker to plant a firm header past Steve Simonsen.
A quick break provided Garner with a chance to complete his hat-trick soon after, but Simonsen dived low to his left to make a routine save.Cresswell and substitute Mark Yeates saw opportunities go begging as Sheffield threw men forward in the closing stages.
The Blades ran out of steam as the full-time whistle approached, however, and their misery was compounded by the late dismissal of Lowry, who brought down Garner as he broke clear.