Billy Sharp scored the goal that earned the Blades victory in the first South Yorkshire derby of season.
The skipper fired over a Jack O'Connell cross in an impressive encounter, which saw United's Leon Clarke and Barnsley's Angus MacDonald sent off.
Boss Wilder made two changes to his starting line-up for the lunchtime game. Stearman was ruled out with a hamstring problem and Wright took over, whilst Duffy was preferred to Carruthers in midfield.
The pace early was frenetic and the impetus with United as boss Wilder had his side fired up for the derby. The home team won a numerous corners and whipped in crosses from both sides, whilst chances were created. On six minutes, following a quick throw, a low Stevens cross was perfect for Sharp but goalkeeper Davies was ideally positioned to block. Soon after, a free-kick on the edge of the box saw Duffy's shot deflected over.
Barnsley's only noteworthy effort saw Hammill pull a shot wide after a breakaway but the Blades deservedly grabbed the lead on 17 minutes. O'Connell overlapped on the left and provided the cross for SHARP to beat Davies on this occasion, the Tykes goalkeeper failing to keep the ball out after scrambling across his goal.
The mid-section of the half saw Barnsley get back into the game as the early pace dwindled. Chances, though, dried up with both sides guilty of wasting the final pass in potentially dangerous areas.
The action heated back up just before the interval, however, when Clarke and MacDonald chased Fleck's through ball. The duo tangled and squared up to each other and after referee Robinson consulted with one of his assistants, the Blades striker and Barnsley skipper were both shown the red card.
Before the half-time whistle United got back on top, with Duffy heavily involved and he laid off to Fleck, whose shot from the edge of the box was blocked by Jackson, just in front of his own goalkeeper. There was one last Blades chance before the break but O'Connell headed Duffy's free-kick just wide.
Barnsley made a double change at the interval but Duffy remained a constant thorn in the visiting team's side, although it was O'Connell who tried his luck with two long-range shots.
Duffy dragged a shot wide just before the hour, following a move that involved five of his team-mates, whilst the visiting side's first opportunity of the second half saw Potts head a near-post corner over. Potts tried to level once again on 62 minutes but his blast from the edge of the box was blocked by Wright.
The Blades were quickly back on the offensive. Basham overlapped down the right and his low cross saw Sharp get a touch but he was unable to turn the ball towards goal. A tiring Duffy received a standing ovation when he was replaced by Brooks, who was quickly embroiled in the action.
Brooks beat Pinnock but his shot was blocked and then the young substitute went closer still on 70 minutes. From a Stevens cross, Brooks beat his man at the near post but Davies saved with his backside and the ball spun along the goal-line before nudging the far post.
Davies saved again soon after, just managing to tip over O'Connell's header from Fleck's corner and Sharp also received a great reception when he made way for Evans with 15 minutes to go.
Late on Barnsley tried to push the Blades back but shots from Potts and Hammill were wild and Ugbo's attempt to turn in the box, following a cross from the right, was marshalled by the dependable Wright as United chalked up a clean sheet and three more valuable points.
Blades: Blackman, Stevens, Fleck, O'Connell, Basham, Clarke, Sharp (Evans 75), Wright, Coutts, Freeman, Duffy (Brooks 66).
Unused: Lundstram, Lafferty, Eastwood, Brayford, Carruthers.
Barnsley: Davies, McCarthy (Ugbo 45), Williams, MacDonald, Hammill, Bradshaw (Thiam 79), Moncur (Pennock 45), Jackson, Potts, Pearson, Hedges.
Unused: Townsend, Barnes, Mowatt, Bird.