Eagles scored after Shaun Derry conceded a needless foul with just eight minutes gone.
Neil Sullivan brilliantly saved a David Graham header, while Leeds substitute Robbie Blake shot inches wide.
Paul Butler then headed over and David Lucas saved Rob Hulse's header for Leeds, while Wednesday's Chris Brunt hit the post from 20 yards.
Leeds boss Kevin Blackwell:
"They caught us cold. One or two of our lads didn't get up to derby pace and it was a really poor goal to lose the game to.
"But all credit to them. They played with a tremendous spirit and got great
backing from the crowd.
"If you get them going here it's a tremendous place, but we created enough chances to get something."
Sheff Wed: Lucas, Simek, Coughlan, Hills, Wood, Whelan, O'Brien, Brunt (Rocastle 83), Eagles, Peacock, Graham (Bullen 72).
Subs Not Used: McGovern, Ross, Corr.
Goals: Eagles 9.
Leeds: Sullivan, Kelly, Butler, Gregan, Crainey, Lewis, Einarsson (Richardson 63), Douglas, Derry, Healy (Blake 67), Cresswell (Hulse 71).
Subs Not Used: Bennett, Kilgallon.
Ref: P Taylor (Hertfordshire).