United suffered a second consecutive defeat in Millwall's Den.
David Brooks was on target for the Blades with an impressive side-foot volley but United left the capital with nothing.
Leading scorer Clarke was handed the captain's armband as boss Wilder made two changes. Stearman and Brooks returned to the starting line-up with Wright and regular skipper Sharp dropping to the bench. There was also a place amongst the substitutes for Heneghan.
Stearman was involved in the first action, getting across to snuff out Gregory's opportunity after Morison and Wallace combined. United's first chance saw Lundstram cut back on to his left-foot but his shot hit Brooks and drifted wide. In a frustrating start for Brooks, he was booked on ten minutes when referee Madley thought the youngster dived following a collision on the edge of box.
Basham blocked a Ferguson shot destined for the bottom corner and Millwall's start was rewarded on 14 minutes when the ball broke nicely for GREGORY, who produced a neat turn before slotting past Blackman.
United's best move of the opening half hour saw Fleck's crossfield ball controlled by Basham but the subsequent low side-foot from Brooks was saved by Archer. Basham was finding space on the right flank but a number of inviting first half crosses failed to find a Blades shirt.
A Fleck shot was blocked and in an action-packed first half Blackman made a tremendous save, pushing away a Saville shot after Meredith's long throw caused problems.
United then levelled with the final opportunity of the first period. Lundstram robbed Hutchinson, enabling Duffy to lift a pass over the defence and BROOKS did the rest - side-footing a volley past Archer and into the top corner.
The goal lifted the Blades and the start of the second half saw Millwall permanently on the back foot for a period. Fleck had a shot blocked by Cooper and fire two more off target and a Brooks curler was headed away.
There was another Duffy effort, which was off target, before Millwall regained the lead with their first attack of the half. O'Connell was dispossessed as he brought the ball out of defence and after Stevens failed to cut out Gregory's pass, ROMEO had the space and time to beat Blackman.
Wallace had a chance to net a third but he was crowded out after taking on Carter-Vickers and Lundstram, then Cooper went close to connecting with Ferguson's free-kick.
Sharp and Donaldson were introduced as United chased a leveller but Millwall professionally took the sting out of the game by denying the visitors any sight of their penalty area.
And the home side secured the points with a third on 87 minutes. From Wallace's free-kick from the left, COOPER rose at the back post to head in off the crossbar, seemingly the goal-line technology helping referee Madley and his assistant award the goal.
It was the signal for a number of the 1,883 Blades fans inside The Den to make their long trip back north.
Millwall: Archer, Meredith, Hutchinson, Gregory (Thompson 76), Ferguson (Craig 85), Romeo, Wallace (O'Brien 90), Tunnicliffe, Morison, Saville, Cooper.
Subs: Mbulu, King, Twardek, Elliott.
Blades: Blackman, Stevens, Fleck, O'Connell, Basham, Lundstram (Donaldson 82), Clarke, Stearman (Sharp 73), Carter-Vickers, Duffy, Brooks.
Subs: Moore, Wright, Heneghan, Lafferty, Carruthers.