Two late goals from Shaun Miller fired the Blades into the third rond of the FA Cup with Budweiser.
It appeared that Tom Pope's first half goal would be enough for Port Vale to secure victory but Miller struck after 90 and and 90+4 to secure victory on a cold December afternoon.
Westlake and McAllister started for the Blades, replacing McMahon and McDonald. Former Blades Academy player, James was named in Vale's midfield.
The formation remained 4-4-2 with McAllister a straight replacement for McDonald but it was the suspended midfielder's namesake, Vale defender Clayton, who caused the first problem, diverting the ball at his own goalkeeper from Porter's cross on four minutes.
Blackman's half-volley, on 14inutes, was goalbound until a decisive deflection off McDonald, whilst a difficult Porter header from distance was straight at goalkeper Neal. Port Vale's first serious chance came from a long throw but Pope poked wide on 28 minutes and it was followed by Long blocking from Williamson after a through ball by Pope.
Flynn tried his luck from distance but United were behind following a mistake on 33 minutes. Maguire's pass inside was cut out and after a spell of nervousness in the box, POPE slotted past Long before heading off to celebrate with his boss on the touchline.
Before the break, the Blades were unable to get back on level terms but the home side were the more attacking force. A Blackman free-kick was deflected wide, whilst in stoppage time at the end of the half Porter was edged away from a Maguire cross by McCombe but no penalty was forthcoming.
The Blades were forced into a change at the break, Collins replaced by Williams with Hill switching to central defence but the first two chances of the second period fell to Miller. Firstly he was denied by a point-blank save from Neal and then shot wide on the turn - both the result of crosses from Doyle.
A powerful Blackman shot on 63 minutes, after cutting in from the right, was straight at Neal, whilst Wilson sent on more attacking intent when Cofie replaced McAllister. Neal again denied Blackman after a link up with Flynn and Maguire headed over a corner as the Blades continued to force the visitors back.
Cofie fired over from distance and Blackman was unable to keep a 20-yard free-kick down, whilst as the game entered the final ten minutes United missed a golden chance. Blackman, a threat to Vale all game, provided the cross but Miller's header from six yards was into ground and over.
Port Vale's first chance of the half, on 83 minutes, was from Burge but Long's save began another Blades move but Blackman fired into the sidenetting. Wilson's last throw of the dice was to replace Porter with Cresswell, who quickly beat Neal in an aerial battle but the drama continued as the watch ticked around to 90 minutes. Flynn's inswinging cross was flicked beyond the Vale goalkeeper by MILLER, who was one of three Blades players in a position to score.
Four minutes of added time was announced and the Blades were again the attacking force but the only danger for Vale was a Miller cross, after Blackman's trickery, but Neal held...something he couldn't do in the fourth minutes of added time.
Again the game was ticking around to a climax when Flynn's shot was parried by Neal, Cresswell managed to get a toe to the ball and direct it perfectly for MILLER to slide home. The striker whipped off his shirt to celebrate and was subsequently booked, although at the precise moment he didn't seem particlarly bothered!
Blades: Long, Westlake, Maguire, Hill, Flynn, Doyle, Porter (Cresswell 87), Blackman, Miller, Collins (Williams 45), McAllister (Cofie 66).
Unused: Philliskirk, Ironside, McFadzean, Coyne.
Vale: Neal, Yates, McCombe, Myrie Williams (Dodds 76), Vincent (Taylor 85), Pope, McDonald, Williamson (Andrew 76), James, Burge, Duffy.
Unused: Loft, Johnson, Shuker, Davis.