A stunning volley from Kalvin Phillips had drawn Leeds level in the 34th minute after Billy Sharp’s second-minute opener for a Blades side who ran riot in the first half.
Leeds were then denied by the post after a fine effort from Samu Saiz after the break but the Blades had the last laugh thanks to a clinical finish from Brooks who had only been on the pitch for six minutes.
At a full house Elland Road, Leeds got off to a nightmare start as Sharp gave the Blades a second-minute lead with their first attack.
From a throw in on the right flank, Duffy delivered a sweeping cross which caught United’s defence flat-footed and allowed Sharp to ghost in and head the ball home from close range.
Leeds could not get going and Leon Clarke prodded a good chance just wide from another dangerous Duffy cross before Luke Ayling then made a crucial clearing header to clear as Enda Stevens lurked in behind.
A George Baldock shot from the edge of the area was then saved by Andy Lonergan with Leeds only threatening through deliveries from free-kicks and mainly through Gjanni Alioski down the right flank.
And only a superb save from Lonergan denied the Blades a second in the 26th minute as the experienced goalkeeper brilliantly tipped over a point-blank effort from Sharp following Leon Clarke’s cross.
Leeds were going nowhere but that all changed in the 34th minute when a cross from Alioski eventually fell to Phillips who unleashed a stunning 20-yard volley that gave Jamal Blackman no chance in the Blades net.
But the visitors were then only thwarted a quick reply one minute before the interval by more superb goalkeeping from Lonergan who somehow kept out an effort from Sharp who had been found free in the area by Duffy’s quickly taken free-kick.
The Blades were then straight on the attack after the interval and Pontus Jansson was brought on for Liam Cooper who appeared injured 11 minutes after the restart.
And seconds later only the post deniedSaiz a wonderful goal as the Spaniard let fly from the edge of the box with a beauty that beat Blackman but not the woodwork.
Soon after, Phillips then appeared lucky to pick up just a yellow card after catching Baldock late on the right touchline.
But Leeds then squandered a fine chance in the 68th minute when a Saiz cross presented Alioksi with a free header which was placed straight at Blackman from inside the box.
And that miss was to prove extremely costly in the 81st minute when the Blades poured forward to score the winning goal through substituteBrooks who had only been on the pitch for six minutes but was afforded too much space by the Whites defence and took full advantage by rifling a rocket of a shot past Lonergan.
The Blades could and should have scored seconds earlier in any case through Clarke who put a low shot straight at Lonergan when well placed.
And there was little response from Leeds who were unable to find an equaliser despite five minutes of added time.
Leeds United: Lonergan, Ayling, Pennington, Cooper (Jansson 56), Anita (Grot 83), Phillips, O’Kane, Vieira, Saiz, Alioski (Hernandez 70), Lasogga. Subs not used: Wiedwald, Shaughnessy, Jansson, Roofe, Dallas.
Sheffield United: Blackman, Baldock, Stevens, Fleck, O’Connell, Basham, Clarke, Sharp (Brooks 75), Coutts, Carter-Vickers, Duffy (Lundstrum 85). Subs not used: Moore, Donaldson, Wright, Lafferty, Carruthers.
Referee: Scott Duncan.