Ben Davies smashed home the late winner as United picked up their first points of the Sky Bet League One campaign.
The winger fired over with six minutes to go as Peterborough dropped their first points of the season.
Jose Baxter gave United the lead and Shaun Brisley levelled before Davies struck the decisive blow.
Boss Clough made no less than five changes for Tuesday's fixture. Collins, Baxter, McNulty, McEveley and Doyle, who took the captain's armband, all started. Harris, Flynn, Reed and Higdon dropped to the bench and there was no place for Scougall. Alcock is formerly of Peterborough and the home team included former Lane loanee Mendez-Laing.
The early exchanges suggested the Blades were operating with a regular 4-4-2 system but the home side were first to work a chance. Howard rushed out of his goal and was beaten by Washington, who then skipped around Collins but the referee ignored the striker's fall.
Washington was lively in the opening minutes and had already shot weakly at Howard before he got clear on 10 minutes but on this occasion he was put under pressure by McEveley at the vital moment and half-volleyed over.
Coincidentally, former Posh defender Alcock had United's first two chances. On 15 minutes, a corner from Davies beat a number of bodies and Alcock swung and missed with his effort and moments later he fired over after Murphy's lay-off.
Taylor struck the outside of a post with an effort from an acute angle before the Blades took the lead with a move which deserved a goal on 25 minutes. McNulty, Baxter and Davies were all involved in crisp passing before the latter's touch enabled BAXTER to slide the ball across the goalkeeper and into the corner of the net.
Peterborough did not spend long licking their wounds. Anderson cut inside and fired over before the home side levelled on 34 minutes. Taylor's near post corner saw BRISLEY powerfully head home with Collins and Howard, who may have been held back, left in a heap on the deck.
Further Posh changes saw Payne fire over the top and Washington kept out by Howard, who was quickly off his line, but the last kick off the half saw Baxter almost double his tally, his effort, though, was deflected wide.
Chances came thick and fast at the start of the second half. Vassell fired just wide after a Posh move began with referee Duncan tackling Davies, whilst United hit back with a couple of efforts. Penalty appeals were turned away when McGahey was pushed off the ball from a Davies corner and then Basham was just wide after McNulty beat Santos on the left.
Taylor struck the outside of a post on 53 minutes from Washington's pass and Mendez-Laing shot straight at Howard, whilst the relentless action continued at the other end. From Alcock's long throw, Basham flicked on and Baxter could not get enough on his header to test goalkeeper Alnwick - a moment later McNulty was snuffed out by Santos as he was about to pull the trigger.
On 65 minutes the travelling fans thought United had regained the lead when Basham tucked away Baxter's prod forward but a linesman adjudged the midfielder to be offside and then Murphy shot tamely at Alnwick.
A number of substitutions, including Higdon replacing McNulty, preceded a good chance for Barnett but he was unable to turn Washington's free-kick towards goal on 72 minutes.
Into the final ten minutes Payne fired over from distance and Flynn took over from Baxter with Murphy switching to a central role. The vital moment, however, arrived with six minutes left of normal time. A throw on the left saw Higdon battle for possession and the ball spurted out to the edge of the box where DAVIES was ideally placed to smash into the bottom corner.
Four added minutes was announced as United looked to protect Howard's goal and the men in red and white were solid late on ahead of the final whistle from referee Duncan - signalling the first points of the campaign.
Peterborough: Alnwick, Smith, Ntihe (Ferdinand 75), Brisley, Taylor (Barnett 71), Payne, Vassell, Washington, J. Anderson, Mendez-Laing, Santos (Burgess 63).
Unused: Day, McCann, Newell, H. Anderson.
Blades: Howard, Alcock, Basham, Doyle, Murphy, Baxter, McNulty (Higdon 72), Collins, Davies, McGahey, McEveley.
Unused: Harris, Butler, Flynn, Campbell-Ryce, Reed, Turner.