After falling behind in the first half, the hosts fought back superbly to hold a 2-1 lead going into the final few minutes, thanks to goals from Josh Morris and Duane Holmes.
However, the visitors struck back and levelled things up through a Billy Sharp penalty late on to earn a share of the points.
Graham Alexander made just one change to the side which began the game against Charlton Athletic, with Richie Smallwood taking the place of Paddy Madden.
The first real meaningful chance of the match went the way of the home side on four minutes. After Holmes and Jordan Clarke had worked a short corner well, the latter stood the ball up for a towering Murray Wallace, who glanced his header wide of the post.
Another headed opportunity was then spurned moments later, this time by the Blades, as Jack O’Connell rose highest but just couldn’t keep the ball down.
Chances were in short supply, and it took until the 23rd minute for the Iron to create another of note. Van Veen initially did well but, after he’d shrugged off his marker, his shot from the edge of the area was deflected into the arms of Blades ‘keeper Simon Moore.
A much more clearcut opening then came the way of the Dutchman just after the half hour mark, with a ball through getting him in behind the visitors’ back four. Van Veen then lashed an effort goalwards. However, it was always rising, as it flew over the crossbar.
Ten minutes before the break though, Chris Wilder’s team were ahead. A well-worked set-piece on the edge of the area left Chris Basham with the simplest of tasks, as he slotted home from close range.
Holmes had another attempt just minutes prior to the interval, but United would go in trailing to Basham’s strike.
Scunthorpe lifted the tempo after the restart, and nearly levelled things up immediately. It was through Smallwood, who curled a right footed shot into the arms of a diving Moore from 18 yards out.
That positive start was soon rewarded, with Morris rifling a strike past Moore at his near post. The winger wasn’t picked up by the Blades’ defence, and following a strong run into the penalty area, the League One August player of the month did the rest, to send the home crowd into hysterics.
Morris’ equaliser really did light the blue touch paper, as both sides went in search of a second in the minutes after the goal. It was a goal Scunthorpe went close to getting on the break, as Holmes sprinted down the field following some great defensive work initially by the Iron backline. The American couldn’t pick out a man though, and had to watch his efforts come to nothing.
A twist then followed, when the Blades’ first goalscorer Basham saw red for a challenge on Neal Bishop in the middle of the park.
Alexander’s side then almost made the numerical advantage pay straight away, and would have done if not for some good goalkeeping from Moore. It was a case of deja vu as Morris drove an effort at him from close range, but this time he responded, as he parried the ball away.
The pressure did eventually pay off and, with nine minutes left on the clock, Holmes got his first goal for the club in some style. Having picked up the ball just inside the field on the right, the United man drilled the ball past a scrambling Moore, and into the far corner, to complete the turnaround.
Wilder’s men refused to give in despite being down to ten men however, with their efforts earning them a penalty moments later, when David Mirfin was penalised for a foul on substitute Stefan Scougall. Former Iron striker Billy Sharp then stepped up, and fired the ball past Luke Daniels, and into the roof of the net.
Sharp’s strike would go on to be the final act of the match as, in spite of their best efforts, the hosts just couldn’t find that all important third.
Scunthorpe United: Daniels, Wallace, Mirfin, Dawson (Madden 81), van Veen (Hopper 81), Morris, Bishop, Toffolo, Smallwood, Holmes, Clarke.
Substitutes not used: Anyon, Wiseman, Adelakun, Mantom, Goode.
Sheffield United: Moore, Fleck, O'Connell, Basham, Sharp (Lavery 90+2), Done, Coutts, Freeman, Ebanks-Landell, Duffy (Scougall 76), Lafferty.
Substitutes not used: Ramsdale, Hussey, Brown, Whiteman, Chapman.