The first Steel City derby since 2012 saw United dominant and increase the gap over Wednesday in the Championship table.
Leon Clarke scored twice, whilst John Fleck and Mark Duffy were also on target.
There were a couple of surprises in the Blades team after a week of injury headaches for boss Chris Wilder. In total there were three changes with Carter-Vickers, Baldock and Clarke included. Freeman missed out with an injury sustained in the home fixture with Norwich, whilst Moore and Sharp were deemed fit enough for the bench.
Brooks may not be well-known in S6 but he took just two minutes to make a significant impact in front of the Hillsborough Kop. His mazy run took in three or four defenders before he was fouled on the edge of the box. Brooks then back-heeled the set-piece for FLECK to side-foot low into the net, with goalkeeper Westwood rooted to his spot.
Wednesday soon had a chance to respond with a free-kick in a similarly dangerous area following a Wright foul but the shot from Jones flicked off the wall. Bannan then chipped over the United defence but Reach was overstretching as he went for the ball.
On 13 minutes Clarke beat the offside trap to attach himself to Fleck's pass but his effort was weak - the former Owls striker was more forceful with the next opportunity, though.
The referee's watch ticked around to 15 minutes when Stevens's ball over the top resulted in CLARKE again getting clear and this time he slipped the ball beyond Westwood and into the net.
Apart from the top tier of the Leppings Lane end, Hillsborough went scarily quiet as they reacted to the scoreline. The action remained high tempo but the chances dried up for a spell. United won a number of corners and from one Brooks recycled possession but Basham, playing in midfield, volleyed over.
As half-time approached, Wednesday applied a bit of pressure - a powerful Hunt shot looked on target but Wright deflected the ball with his head and after the Blades failed with a number of attempted to see out the half, Wallace flicked inside for HOOPER, who got to the ball before Wright to divert home at the near post. It was the last action of a pulsating first half.
Wednesday made a change at the break and their goal before the interval gave them impetus to apply more pressure. The chances, though, were coming at the both ends. Brooks was well off target after Fleck got the better of Bannan and Hooper was in the clear from Reach's pass but his mis-control allowed Blackman to collect.
Just after the hour, the game sparked back into the life. Brooks nutmegged Hunt and played in Clarke but the striker fired over and United made their first change - Duffy replacing Wright as the formation changed.
Wednesday levelled on 65 minutes as Carter-Vickers failed to cut out Reach's cross and JOAO emphatically hammered past Blackman from inside the box.
The home fans were still celebrating when the Blades retook the lead less than two minutes later. The goal belonged the individual brilliance of DUFFY, who twisted and turned his marker before lashing past Westwood at the goalkeeper's near post.
Bannan fired a half-volley wide, whilst Brooks went close again, he got the better of Bannan and Reach before forcing a fantastic save out of Westwood.
A fourth Blades, goal, though, wasn't far away. On 77 minutes Wednesday failed to clear, Coutts and Brooks were both involved before CLARKE outmuscled both of the home central defenders before lifting over Westwood and into the goal.
It was the signal for some home fans to leave. Hooper's header from Hunt's cross was comfortable for Blackman and the Wednesday scorer also had another effort deflected wide by O'Connell.
By contrast, the Blades fans were in full voice...right up to the final whistle and beyond. And why not.
Owls: Westwood, Hunt, Van Aken, Lees, Reach, Wallace (Butterfield 77), Jones (Joao 45), Lee, Bannan, Fletcher (Rhodes 67), Hooper.
Unused: Wildsmith,Palmer, Nuhiu, Pudil.
Blades: Blackman, Baldock, Stevens, Fleck, O'Connell, Basham, Clarke, Wright (Duffy 62), Coutts, Carter-Vickers, Brooks (Lundstram 84).
Unused: Moore, Sharp, Lafferty, Evans, Carruthers.