After an even first-half, the South Yorkshire outfit went ahead in the 51st minute as Sharp’s instinctive strike from a Jay McEveley corner was enough to bag the points.
United made one change to the side that secured a place in the third round of the FA Cup on Tuesday evening, with Tommy Rowe replacing Jamie Ness in the starting line-up at Glanford Park.
Meanwhile ex-Iron winger Martyn Woolford was also named in the Blades team, who were managed in the away dugout by Nigel Adkins.
It was the visitors who were first to threaten as Woolford swung in a deep free-kick towards Dean Hammond, who was left unmarked at the back post but could only hit his attempted volley over the crossbar.
Defender John Brayford also tried his luck from distance with a fierce effort that stung the palms of Luke Daniels, though he was able to hold on as a number of opposition players readied themselves to pounce on any rebound.
Excellent work from Scott Wiseman then saw United construct their opening opportunity of the game as he managed to hook in a cross under pressure and after a little chaos in the box, Tommy Rowe struck for goal.
His shot was pushed away by George Long and Kyle Wootton was just unable to capitalise on the loose ball before it went out and play was eventually restarted with a goal-kick.
Robins’ men were beginning to take control of the contest and went close again as a Luke Williams corner was met by the recently prolific Jack King but his header into the ground landed nicely into Long’s gloves.
Paddy Madden then had a chance as he darted in front of his marker and was found by Scott Laird in the area, though couldn’t quite connect with the fullback’s centre.
The Iron pressure was mounting and a clever set-piece saw Williams force Long into further work but a quick throw out from the ‘keeper initiated a dangerous looking counter-attack.
Midfield man Paul Coutts was put through and lashed a right-footed drive at goal that Daniels did superbly to divert behind in what was arguably the best move of the first-half.
Blades striker Sharp had his first attempt of the match as the clock ran down on the opening period, controlling the ball before smashing a long range shot which flew marginally over.
A superb last ditch block from Niall Canavan denied Chris Basham and that was the final action of the half as referee Andy Haines brought things to an end with the score still goalless.
The visitors came out stronger after the break and got themselves very much on the front foot.
First, Brayford’s low cross was met by Woolford, who had a powerful drive pushed away by Daniels and then Sharp smashed one from distance that the United shot stopper hung onto.
Sharp’s cross-cum-shot was also hacked away by Charlie Goode, with Matt Done waiting to finish, before the pressure told and the deadlock was broken.
Captain McEveley’s flag kick was tucked away by Sharp to put Adkin’s side ahead after what had, in fairness, been an electrifying start to the second forty five by the Blades.
The Iron responded by conjuring up an attack of their own as Rowe motored forward before feeding Madden, whose venomous strike was just about collected by Long.
That man Rowe then came within a whisker of bagging an equaliser as Williams’ accurate ball into the middle found the loanee and his resultant poke had the goalkeeper flat footed but went just wide of the upright.
Much like the way the opening half had begun, United were starting to come back into the clash and Willams, ever a menace, drew Long into a fine stop as his 30-yard strike was tipped away when it looked for all the world to be heading into the top corner.
Williams turned provider once more as he teed up substitute Hakeeb Adelakun on the edge of the area but the wide man’s volley whizzed harmlessly into the stands.
Both Darius Henderson and Ness were introduced as the clock ticked away but clear goal scoring chances were starting to dry up as the Blades attempted to close thing down.
Despite a succession of second-half chances, including a headed opportunity for Charlie Goode following a quick corner late on, the Iron couldn’t find a leveller and 1-0 was how it remained.
Scunthorpe United: Daniels, Wiseman, Goode, Canavan, Laird, King (Henderson, 76), Bishop (Ness, 82), Rowe, Williams, Madden, Wootton (Adelakun, 60).
Substitutes not used: Anyon, Clarke, Dawson, van Veen.
Sheffield United: Long, Brayford, Edgar, Collins, McEveley (Wallace, 83), Coutts, Hammond, Basham (Reed, 73), Woolford, Done (Sammon, 64), Sharp.
Substitutes not used: Howard, Flynn, Scougall, Campbell-Ryce.