Two late goals put paid to United's six-match unbeaten run.
Matt Done's second half header looked set to give the Blades victory but goals after 88 and 90 minutes secured Peterborough's win - Jack Payne and Conor Washington on the scoresheet.
Boss Clough made one change for the fixture with Peterborough. McNulty returned to the starting XI at the expense of Kennedy, who was injured on Saturday. Alcock and Holt were added to the bench.
For the first home game since the passing of the well-known and popular fan, David 'Shred' Spencer, the players wore black armbands and there was moving tribute just before kick-off.
In a subdued atmosphere, United made the brighter start. From the edge of the box, McNulty's shot was pushed over by goalkeeper Alnwick and Harris curled over the top corner. Peterborough's first chance saw Newell put Vassell in behind the Blades defence but the subsequent shot was into the sidenetting.
Alnwick was also called upon to save from Murphy and Doyle but the Posh goalkeeper would have been powerless to stop United's best move of the first half on 32 minutes. It began with a 60-yard diagonal ball from Basham to Murphy and concluded with Done, unmarked at the back post, almost attaching himself to a Harris cross.
Late in the half was Peterborough's best spell before the interval. Coutts was caught in possession but Vassell fired over and after Done failed to clear, Turner was forced to push away a half-volley from Ntlhe.
Holt replaced at the start of the second half and in a sluggish start for both teams, Vassell fired over for the visitors before Murphy cut inside and fired wide for the home side.
Just after hour mark Reed took over from McNulty and the teenage midfielder played a part in the opening goal moments later. He delivered a long ball down the left channel which defender Santos looked in control of but he was robbed by DONE, whose first effort was saved by the feet of Alnwick, but the rebound was directed home in front of the Kop by the striker's looping header.
Peterborough hit back, expectedly, and went close on 74 minutes. Bostwick's tackle on Murphy won possession and Payne's 30-yard shot hit the outside of Turner's right post.
The visitors were attempting to use their aerial advantage to get back in the game. Mclean's header from Taylor's free-kick was deflected wide and Basham blocked from Ntlhe after another corner.
In the final ten minutes Freeman replaced Done and Peterborough threw caution to the wind, Santos was added to the forward line. Harris blocked from Newell but United were tiring and Flynn was struggling after all three substitutions had been made.
Peterborough's pressure finally paid off on 88 minutes. A simple pass inside by Taylor found PAYNE in space and his 30-yard shot nestled into the bottom corner.
The drama was not over. Just as four minutes of injury-time was being announced, McEveley and Basham failed to deal with ball down the right channel and WASHINGTON raced on to hammer past Turner.
Late on Basham was added to United's front line but apart from Doyle slicing over a Reed corner, the Blades were unable to put further pressure on Alnwick's goal and the fixture ended in disappointment.
Blades: Turner, Harris, Brayford, Basham, Flynn, Doyle, Murphy, McNulty (Reed 63), Done (Freeman 81), Coutts (Holt 45), McEveley.
Unused: Alcock, Willis, Adams, Calvert-Lewin.
Posh: Alnwick, Smith, Ntlhe, Bostwick, Taylor, Payne, James (Mclean 78), Vassell (Washington 56), Newell, Santos, Zakuani.
Unused: Burgess, Norris, Anderson, Henry, Beautyman.