The Blades, with seven first-team players still sidelined through injury, have now won only one of the last seven league games and trail sixth-placed Leicester by seven points with six games remaining.
The home faithful once again vented their frustration with a chorus of boos towards the under-fire Blackwell at the final whistle.
Scunthorpe have climbed eight points clear of the drop zone thanks to Hayes' 12th goal of the season, which secured Nigel Adkins' side a third straight league win.
Striker Darius Henderson and winger Mark Yeates returned for the Blades and Scunthorpe also made two changes, with McDermott and Michael Raynes earning recalls.
Both sides struggled for fluency in the opening exchanges, but the Blades looked to force the issue and Henderson was wide with an early header.
Scunthorpe defender David Mirfin rescued the visitors in the 20th minute when he blocked Paul Connolly's shot on the goalline and Yeates headed over from Richard Cresswell's shot soon after.
The Blades were given a big let-off in the 31st minute.
Nyron Nosworthy's back pass was woefully short and visiting striker Garry Thompson pounced to race clear on goal, only to fire straight at Blades goalkeeper Steve Simonsen.
Harper curled a right-footed free-kick inches wide for the Blades, but impatient home fans groaned in unison at having to endure more dour first-half action when four minutes of time added on was displayed.
Those groans then turned to jeers of derision as Scunthorpe midfielder McDermott wriggled his way into the area and set up Hayes, who steered the ball underneath Simonsen from eight yards for an unlikely breakthrough.
Yeates' free-kick, after Grant McCann had tripped Quinn on the left corner of the area, forced visiting goalkeeper Joe Murphy into a smart save 10 minutes after the restart.
But it was all uphill for the home side and Blackwell sent on striker Henri Camara for Harper in the 53rd minute.
Glen Little then replaced Yeates as Blackwell looked to turn the game around, while Scunthorpe sent on Michael O'Connor for McCann.
Blades defender Kyle Bartley headed Connolly's free-kick over the crossbar in the 64th minute as the home side stepped up the tempo.
But Scunthorpe almost doubled their lead soon after, with Thompson bursting on to McDermott's through-ball and forcing Simonsen into a fine save.
Referee Russell Booth then waved away Scunthorpe's penalty appeals when substitute Jonathan Fortune went tumbling in the box, while Henderson's header from Montgomery's ball in grazed the Iron crossbar.
The Blades huffed and puffed in the closing stages, but lacked the cohesion to open-up a determined Scunthorpe rearguard despite five more minutes of time added on.