The under-pressure United manager now has two games, a Championship clash at West Brom on Tuesday and an FA Cup battle against Middlesbrough in seven days' time, to save his job.
Scunthorpe, looking for their first ever win at Bramall Lane, were reduced to ten men after just nine minutes when Rob Styles red-carded Grant McCann after the midfielder appeared to stamp on loan signing David Cotterill.
The Blades, fielding the £6.2million strike-force of Rob Hulse and James Beattie for the first time after Beattie's recovery from injury, squandered half-chances with Cotterill and Gary Speed both firing wide.
Scunthorpe pushed forward and almost got the breakthrough in the 39th minute, midfielder Jim Goodwin cutting inside from the left flank before firing in an angled drive from 16 yards, the ball flashing inches wide of the far post as they gained in confidence.
United, scrappy and struggling to find their rhythm, threw away another opportunity, Speed steering his tame header straight into the arms of Joe Murphy before battling Scunthorpe caused more panic, Andy Crosby and Paul Hayes having shots blocked in quick succession.
Goodwin tried his luck with a long-range strike, the ball spinning the wrong side of the woodwork as Paddy Kenny scrambled across his line.
Former Scunthorpe striker Billy Sharp, snapped up for £2million in the summer, came on to face his old team-mates in the 60th minute replacing the ineffective Beattie as United looked for a way to break down the stubborn Scunthorpe defence.
Michael Tonge miscued with a 20-yard strike and Murphy made a vital punch to clear a Lee Martin cross before substitute Matt Kilgallon's header crashed against the post from Speed's free-kick.
Murphy tipped Hulse's stinging shot over the bar and Sharp's overhead kick was deflected over the target as United piled on the pressure.