Marcus Tudgay headed Wednesday into an early lead from Tommy Spur's cross and Chris Brunt made it two from 35 yards.
Leeds were given hope when Tudgay saw red for a second booking, but Jermaine Johnson fired in a third minutes later.
Lee Bullen scored an own goal to ensure a frantic finale and Ritchie Cresswell then poked home, but it came too late.
Sheffield Wednesday boss Brian Laws:
"I enjoyed the game apart from the last 10 minutes. "I thought we were excellent, fast out of the blocks and creative. We had a bit of an edge to our game.
"That last five minutes when it got to 3-2 seemed like a lifetime. If you had a heart monitor on me it would have gone right through the roof."
Leeds: Stack, Richardson, Rui Marques, Heath, Lewis, Howson (Blake 46), Douglas, Kishishev (Carole 83), Moore, Healy, Cresswell.
Subs Not Used: Ankergren, Johnson, Foxe.
Booked: Healy.
Goals: Bullen 88 og, Cresswell 89.
Sheff Wed: Turner, Simek, Bullen, Wood, Spurr, Johnson (Small 72), Watson, Whelan, Brunt, Burton (MacLean 84), Tudgay.
Subs Not Used: Adamson, Gilbert, Folly.
Sent Off: Tudgay (49).
Booked: Tudgay, Spurr, Burton.
Goals: Tudgay 7, Brunt 37, Johnson 54.
Att: 25,297
Ref: L Probert (Gloucestershire).
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