Gunnar Halle's lazy back-header, which almost let in David Hirst after two minutes, sparked the game into life, and midway through the first period three goals came in a five-minute spell.
Wednesday looked the more composed early on but Leeds, prompted by the tireless Lee Bowyer, weathered the storm and slowly began to take a grip.
Lee Sharpe scored the first after 17 minutes, firing a low left-foot effort past Kevin Pressman after a pass by Ian Rush. After Brian Deane had gone close to doubling Leeds' advantage Wednesday broke and equalised when Hirst rose above a static home defence to head home Benito Carbone's corner.
A minute later Deane caused pandemonium in the Wednesday defence with Des Walker's hesitancy allowing the rejuvenated Rod Wallace to nip in and force the ball under Pressman for Leeds' second.
The visitors began to assert an awkward control while always looking vulnerable to Wednesday's counter-attacking style, particularly the runs of Mark Pembridge on the left.
Wednesday equalised after 51 minutes when Carbone raced into the Leeds box and gave Andy Booth the easiest of chances to fire past Nigel Martyn. Leeds, boosted by the continuing efforts of Deane and Rush, who revelled in his midfield role, looked the most likely to win it on the break.
George Graham, the Leeds manager, said: "That's probably the best we've played since I arrived here. It was lovely to see a bit of individual quality stuff from people like Lee Sharpe."Reuse content