The former Everton and Portsmouth defender had a dream debut, scoring the winner from the spot and claiming joint Man of the Match with Alan Quinn. The victory by the Blades ended City's run of three wins on the trot.
During that spell they scored 10 goals and conceding none before they met the Blades.
Unsworth will have been delighted with his performance. Having signed on a three year deal last Monday from Portsmouth, he netted the winner with one minute to go after Rep. Ireland international Alan Quinn was tripped in the box by right-back Richard Duffy.
The decision was harsh but non the less fair on the visitors who by that time had already seen their lead which was scored by James Scowcroft on 24 minutes cancelled out three minutes later by Steve Kabba and then later in the second half see Matthew Heath dismissed for two book able offences on the hour mark.
Kabba was not meant to be on the pitch when the game kicked off, team mate Danny Webber was origionally lined up with Neil Shipperley before the game but the former Watford man was forced to end the game with a calf strain leaving Kabba to take the glory.
However an end-to-end first half did not question that this might end up 0-0 as both teams attacked with force. Though it was the visitors who would have the first say. Loan man Willo Flood supplied a neat ball through to JAMES SCOWCROFT and the former Leicester City striker held off Chris Morgan to slash home from eight yards past keeper Paddy Kenny.
After that sucker punch the Blades needed a lift which was spurned on by the fans, and to their persistence were rewarded three minutes later.
Alan Quinn picked up the ball in his own half and having seen STEVE KABBA create a run, Quinn passed through for the former Crystal Palace striker to beat the off-side trap to nail the ball past goalkeeper Stephen Bywater for 1-1.
Neil Warnock's side were finally turning the style on and could have gone into half-time with a lead when Paul Ifill's cross was marginally headed over by Kabba.
In the second half United looked determined to go for the win and lift them to the top of the table but where unable to do so when Bywater produced a World class save from defender Leigh Bromby powerful shot which should have landed in the top right hand corner.
The Sky Blues looked jaded and would have welcomed a point at Bramall Lane but their day got worse when Matthew Heath evaded scorer Steve Kabba in a idiotic challenge which referee Colin Webster sent Heath his marching orders with much delight to the home crowed.
The centre-back had alreday been booked for a similar challenge earlier when he tugged at Neil Shipperley's shirt. City made changes to hang onto a 1-1 draw but unfortunately lost their best player on the pitch when Gary McSheffery was made way for defender Andrew Whing with twenty minutes left.
United's persistence paid off again, still buzzing from their last minute winner inflicted on Preston North End last Saturday.
The Blades were looking for lady luck again and got it when Quinn's charging run forced Richard Duffy into a tackle, his late challenge gave away a penalty.
The Sky Blues accepted the foul without protest and with no Kabba or Webber on the field it was left to debutant DAVID UNSWORTH to take the spot kick. Warnock could not watch as the former England international smashed the ball to his right, Bywater dived the wrong way and it was party time as the majority of the 17,000+ Bramall Lane crowed went mentle.