Two second half goals from skipper Billy Sharp secured three more vital points to keep United amongst the Sky Bet Championship frontrunners.
He netted from close range after crosses from David McGoldrick and Enda Stevens.
Manager Wilder kept faith with the squad that faced Millwall at the weekend, he went with an identical starting XI and substitutes in Lancashire. United had a lot of early possession but were unable to trouble goalkeeper Raya, although a corner routine on six minutes almost presented Sharp with a chance.
A patient move on 25 minutes saw Duffy's shot on the turn parried away by Raya and Sharp's flicked header from a Stevens cross was off target. The home side's first chance saw Reed's acrobatic attempt blocked by O'Connell on the half hour.
Blackburn's forwards were working overtime to keep United's defenders back but the home side were a threat on the break. Reed's pull-back was ideal for Dack but the subsequent shot was deflected away by Egan.
The final chances of the half fell to United but goalkeeper Raya saved O'Connell's header, pushed over from McGoldrick and batted away from Fleck.
Dack headed over early in the second half but United were soon back on top. A break down the right saw Basham get around the back of the home defence but Reed blocked a powerful effort from Fleck.
Bell, Armstrong and Brereton had half-chances for Blackburn but the home side were stung on 66 minutes. United attacked down the left and McGoldrick found himself in space to cross for SHARP, who finished at the second attempt after battling with a defender and the goalkeeper.
The Blades fans had just finished celebrating when Coutts was introduced for his first appearance since last November, the midfielder received a rapturous reception from the travelling contingent.
The next serious chance, on 79 minutes, also came down the left and resulted in a goal. This time Stevens delivered a deep cross and SHARP peeled off his marker to head home at the back post.
United comfortably played out the remaining moments without serious scare. Henderson was ideally placed to save from Armstrong and there was a late chance for a third Blades goal but goalkeeper Raya saved with is feet to deny substitute Washington.
Four minutes of added time passed without incident as United recorded a second consecutive away win.
Blackburn: Raya, Williams, Reed, Smallwood (Mulgrew 45), Armstrong, Graham (Brereton 56), Bell (Rothwell 70), Dace, Lenihan, Evans, Bennett.
Unused: Rodwell, Leutwiler, Conway, Palmer.
Blades: Henderson, Stevens, Fleck, O'Connell, Basham, Sharp (Clarke 82), Egan, Norwood, McGoldrick (Washington 87), Freeman, Duffy (Coutts 73).
Unused: Lundstram, Stearman, Johnson, Moore.