United suffered a first home league defeat since January, facing a well-organised Norwich City team.
Yanic Wildschut scored the only goal, in the first half and despite the Blades hammering the door, there was no way through for Chris Wilder's side.
Brooks made his first league start, he was thrust into the action as boss Wilder contended with a striker shortage. With Lavery, Hanson and Donaldson all injured, it was a blow that Sharp and Clarke missed out after picking up injuries in midweek. Evans started a league game for the first time since returning to the club, whilst Basham, who made his 150th start in a Blades shirt, Freeman and Stevens returned.
From the game's first corner, on two minutes, United registered a chance. Coutts, captain in the absence of Sharp, delivered and O'Connell nodded back into the danger area but a header from Evans was plucked out of the air by goalkeeper Gunn. Norwich's first assault on the Blades goal followed within a minute but Jerome could only find the side-netting following Murphy's run.
Murphy's pace caused United problems when he took advantage of a slack Basham touch but Wright tidied up. Soon after Wright's misplaced pass saw O'Connell help out, blocking from Wildschut.
Brooks was a lively outlet for United, he beat Trybull but Gunn was quickly off his line to save and then the young midfielder chased down a Coutts pass and presented a chance for Evans, but Zimmermann slid in to clear.
The game was end-to-end but that did not work out in United's favour on 23 minutes. A simple pass down the right channel by Maddison resulted in WILDSCHUT firing across Blackman and into the Kop goal.
A first-time side-foot by Coutts and a Duffy free-kick saw the Blades positive in response to the goal, whilst Evans and Brooks both had efforts blocked in the same move as the
home side looked to mount a spell of pressure leading up to half-time.
It continued right up until the break and in the one minute of added time there was an appeal for a penalty following a tackle on Coutts and a Freeman shot, which Gunn smothered.
Early in the second half Fleck tried his luck from 30 yards but Gunn saved and held and the pace from the visitors in wide areas was always a threat. Wildschut's run was ended when Wright blocked but the ball broke to Murphy, who forced a save from Blackman.
With Blades fans feeling aggrieved at a number of decisions not going the way of the home side, the volume was turned up somewhat, especially when referee Duncan removed Wilder from the technical area. The officials were upset that the manager had gone into the opposition's technical area to return the ball!
Two changes in a minute saw Carruthers and Thomas introduced and the Blades remained on the attack, Norwich slowing down proceedings at every opportunity. As the final ten minutes approached Maddison fired straight at Blackman and Fleck was off target for the Blades.
Norwich's appeals for a penalty when Blackman and Maddison clashed were ignored and there were late chances for both sides with Baldock replacing Freeman for United.
Six minutes of added time was added, mainly due to the amount of stoppages and the pace of the restarts. United were continually on the attack but Brooks fired over and it was all the home side could muster despite a spirited attempt - as emphasised by the ovation the Blades players received at full-time.
Blades: Blackman, Stevens (Thomas 74), Fleck, O'Connell, Basham, Wright, Coutts, Freeman (Baldock 86), Duffy (Carruthers 73), Evans, Brooks.
Unused: Lundstram, Carter-Vickers, Lafferty, Eastwood.
Norwich: Gunn, Pinto, Zimmermann, Jerome, Murphy (Husband 60), Klose, Wildschut (Watkins 78), Stiepermann, Trybull, Maddison (Hanley 87), Tettey.
Unused Reed, Vrancic, Hoolahan, McGovern.