In very wet and rainy conditions, the Reds trailed at half-time then Cameron McGeehan levelled early in the second half only for the visitors to go 2-1 up within two minutes before adding another two.
The Reds played some good football at times but their sloppy passing lost the ball in the build-up to several of the goals. A quiet start to the game saw both sides reduced to long-range shots, with visiting goalkeeper Dean Henderson easily gathering from both Cauley Woodrow and Cameron McGeehan who tried their luck from 30 yards.
But it was the visitors who took the lead in the 21st minute when a good move down the right opened up the home defence and Ben Osborn was left totally free on the left of the area to fire in from ten yards out.
Henderson dived to his left to easily hold a 15-yard Woodrow shot but Radlinger was forced into his first save as he parried away an effort from Callum Robinson who had swapped passes with Osborn in another good move.
David McGoldrick came close to doubling United’s lead when his shot from the right of the area took a deflection and bounced off the outside of the right post in the 41st minute.
Oliver Norwood curled a free-kick just wide of the right post early in the second half but it was the hosts who levelled on 55 minutes. A fine pass from left-back Ben Williams allowed Mallik Wilks to play McGeehan clean through on goal and fire into the top left corner just inside the box.
The scores were level for only two minutes as Robinson turned on the edge of the box and found the bottom left corner. Wilks then robbed Oliver Norwood of the ball and ran into the United box but shot straight at the goalkeeper when he could have squared to the unmarked Woodrow.
It was 3-1 on 74 minutes when Callum Robinson volleyed home eight yards out from a fine left-wing cross from substitute Luke Freeman.
The fourth goal was at the end of another excellent move as right-back George Baldock got to the byline on the right wing and pulled the ball back for Freeman to fire in from close range.
Barnsley (4-4-2): Radlinger; Sibbick (Cavare 80mins), Diaby, Andersen (Moon 86), B Williams (Pinillos 80); Thomas (Thiam 63), McGeehan, Mowatt, Wilks (Halme 75); Chaplin (Miller 75), Woodrow (Moore 80). Unused: Collins, Moon. Goals: McGeehan 55. Sheffield United (3-5-2): Henderson; Egan, Basham, Stevens; Baldock, Norwood, Fleck, Lundstram (L Freeman 63), Osborn (Bryan 85); Robinson (Morrison 75), McGoldrick (Sharp 71). Unused: Jagielka, K Freeman, Stearman. Goals: Osborn 21, Robinson 57, 74, Freeman 90.