United exited the Emirates FA Cup at the first hurdle, as non-league Barnet caused a third-round shock on Sunday afternoon.
Shaquile Coulthirst's first-half penalty was enough to settle a contest, in which the Blades struggled to find any real fluency or momentum.
Boss Wilder made ten changes for the tie against the Bees, with only Martin Cranie keeping his place from the New Year's Day win at Wigan. Dowell and Bryan made their debuts, with Coutts captaining the side.
It was Barnet who had the first real sight of goal, but Taylor shot wide, having held off Lundstram. The Bees then thought they had opened the scoring through Coulthirst, who headed home a cross from Alexander, but the assistant referee's flag saved the Blades. United responded but Dowell's goal bound effort was blocked by Sweeney.
The visitors continued to look a threat on the break, this time Stearman had to intervene to deny Coulthirst, before Coutts was yellow carded for a foul and then Robson fired over from distance. On 20 minutes, referee Harrington pointed to the spot after Stearman was adjudged to have fouled Mason-Clark following a counter-attack. From twelve yards, COULTHIRST scored despite the best efforts of Moore, who guessed the right way.
Four minutes later, Bryan was fouled right on the edge of the box, but Dowell's free-kick was blocked, before Coutts saw an effort scrambled away following a short corner. The skipper was again involved, this time firing over, after some neat build-up play. With half-time approaching, United threatened again, but Cousins was equal to Cranie's back post header.
It was again Barnet who were quicker out of the traps after the break, with Johnson required to clear the danger from Coulthirst's low cross, then Moore had to tip a header away for another corner, from which Sweeney was unable to convert despite being unmarked. In the 65th minute, the Blades should have levelled, Dowell picked out Freeman, but he dragged an effort wide of the far post.
Sharp received a warm hand as he replaced Lundstram, before Moore saved to deny Coulthirst. United's number ten looked to make an instant impact, but his effort was collected by Cousins. Sharp continued to look a live threat, but he couldn't divert Freeman's cross past the Barnet goalkeeper from close-range.
The pressure was being cranked up by the Blades, and Clarke's header looked to have beaten Cousins, with Sharp and Duffy involved in the build-up, but the Barnet number one managed to tip it onto the crossbar, as five minutes of added time were signalled, but Barnet held firm to cause a shock at the Lane.
Blades: Moore, Lundstram (Sharp 65), Dowell, Clarke, Coutts, Freeman, Stearman, Bryan (Basham 74), Johnson, Cranie, Washington (Duffy 58).
Unused: Henderson, Stevens, Egan, McGoldrick.
Barnet: Cousins, Alexander, Johnson, Reynolds, Robson, Adams, Coulthirst (Harrison 80), Taylor, Elito (Tutonda 80), Sweeney, Mason-Clark (Fonguck 58).
Unused: Matrevics, Akinola, Walker, Bettamer.