The Reds come out on top in the South Yorkshire derby thanks to Tom Bradshaw's last-gasp header earning José Morais' men a precious three points.
Welsh international striker Tom Bradshaw came off the bench to devastating effect this afternoon when he was on hand at the far post to power home Kieffer Moore's cross and send the Oakwell faithful into raptures.
His 88th minute strike was enough to seal a huge victory in the battle against relegation.
Morais had named an unchanged team for the visit of Chris Wilder's high-flying Blades, the away side making one change, enforced, with Richard Stearman (injured) replaced in the defence by Jake Wright.
The Reds began the game brightly, with Moore sending an early header wide from a George Moncur corner before Moncur himself rattled the crossbar when after a jinking run into the box he unleashed a dipping effort that beat Simon Moore in the away side's goal all ends up but bounced back out off the woodwork.
United had a 10-minute spell of pressure but failed to open the Reds rearguard up.
On 25 minutes Barnsley took the lead somewhat against the run of play when after Moncur's corner was only cleared to the edge of the box, Gary Gardner met it with precision and power and rocketed the ball into the roof of the net.
On 38 minutes United replaced Lee Evans with striker Billy Sharp as they looked for a way back into the match, but the game became scrappy and was 1-0 at the break.
HALF TIME: Barnsley 1-0 Blades
The Reds were fast out the blocks upon resumption of the second half, with Moore and then Isgrove breaking quickly but once Barnsley got to the visitors' box, the moves faltered and huge chances were passed up.
And on 57 minutes, we were made to pay for that profligacy in front of goal.
A scramble of bodies inside the box and eventually it was John Fleck who lashed home with power from 10 yards out leaving Adam Davies with no chance, and the away end went wild.
Adam Hammill replaced Lloyd Isgrove on the hour.
Less than 10 minutes later and the Blades went ahead, the Reds wilting under intense pressure and again after some dubious attempts at clearing the lines, the ball fell for Leon Clarke who buried the opportunity from six yards out with United now looking strong favourites for all three points.
Tom Bradshaw arrived on the scene with 20 minutes left, and five minutes after that Barnsley levelled the game up when Hammill's shot on the left peg was only parried by Moore and there was Oli McBurnie to tap into the empty net for 2-2.
And with 88 minutes played came Bradshaw's moment, his twelfth goal of the season sealing a dramatic and vital Reds victory!
Kieffer Moore did excellently well to volley a cross to the far stick and Bradshaw rose highest to power home the winner in front of a celebrating Ponty End.
FULL TIME: Barnsley 3-2 Blades
Reds: Davies; Yiadom, Jackson, Lindsay, Fryers; Gardner, Moncur (Bradshaw 69), Potts; Isgrove (Hammill 60), McBurnie (Cavaré 90), Moore.
Unused: Walton, Pinnock, Mahoney, Mallan.