Steve Kabba steered Neil Warnock's high flyers to an FA Cup semi-final spot as they chalked up their second cup triumph over Terry Venablesâ€™ side in four months.
United, who had previously dumped the Elland Road side out of the Worthington Cup, stuck in the 78th minute in a scrappy game littered with mistakes.
And Neil Warnock's side, pushing for promotion to the Premiership, effectively ended Leeds season with Venables pinning his hopes on an FA Cup win to steer his side into Europe.
Mark Viduka carved out a half chance in the opening minutes, cutting inside from the left flank before lashing in a shot from the edge of the area that flew high over the Sheffield goal.
Alan Smith almost found a way through in the 19th minute after Viduka let Harry Kewell's pass run to the little striker, he finished with a low shot snapped up by the diving United keeper.
Kewell should have snatched the lead ten minutes later, but his right-foot strike was blocked by the United keeper and when the ball came back Kewell smashed it high and wide.
United danger man Michael Brown found space on the left minutes before half time, cutting inside to fire in a right-foot shot, the ball flying wide of the far post.
Kabba almost broke the deadlock seconds after the restart surging into the area to drill in a stinging right-foot shot pushed over the top by Paul Robinson.
Kenny kept out Viduka sticking out a hand to spoon the ball away from the big striker before Seth Johnson almost grabbed an opener, his fierce drive from 20 yards smothered on the line by the United keeper.
Kabba struck after Michael Tonge's shot had been blocked by Danny Mills, the ex-Crystal Palace striker produced a clinical finish to beat Robinson with a low shot from 12 yards.
Brown nearly added a second, his free kick from the edge of the area tipped over the bar by the visiting keeper.