Ashley Ward fired the home side ahead soon after half-time after the United striker was set up by Michael Tonge.
Jon Harley's powerful free-kick into the roof of the net made it two following a Michael Duberry foul.
Late in the game Ward almost added a third when he powered a close-range header against the bar after Harley had crossed from the left.
Leeds boss Kevin Blackwell:
"The result again highlighted where we are short, and now the club have a decision to make.
"We have to do something because the team needs a lift. When I looked at the bench there was a 16, 17, 18 and a 19-year-old and that is not good enough for Leeds.
"The club has to raise money. But that's not my responsibility, that's the responsibility of the football club. It's clear the club has to do something."
Sheff Utd: Kenny, Bromby, Morgan, Jagielka, Wright, Quinn,
Thirlwell, Tonge, Harley (Lester 90), Gray (Montgomery 90), Ward. Subs Not Used: Francis, Hayles, Forte.
Goals: Ward 50, Harley 64.
Leeds: Sullivan, Kelly, Duberry, Butler, Crainey, Wright, Pugh,
Joachim (Lennon 60), Richardson, Deane, Ricketts (McMaster 66). Subs Not Used: Carson, Carlisle, Walton.
Booked: Duberry, Richardson, Ricketts, Kelly.
Att: 22,959.
Ref: P Dowd (Staffordshire).