Portugal Under-21 international Marco Matias brilliantly lobbed the Owls into a 37th-minute lead but New Zealander Chris Wood equalised in the 61st minute with his second goal in as many games.
Leeds have drawn all four of their Championship games this season and should have made better use of their possession against a Wednesday side who rarely tested goalkeeper Marco Silvestri.
Leeds pair Kalvin Phillips and Gaetano Berardi were cautioned early on for clumsy tackles, the former receiving his yellow card inside 60 seconds as referee Michael Jones looked to impose his authority on a potentially explosive derby.
Leeds were quicker to settle, Stuart Dallas and Mirco Antenucci shooting close from distance and the latter being flagged offside after running on to Sam Byram’s intelligent through ball.
Yet it was Wednesday who struck in the 37th minute. Vince Sasso’s long high pass caught out the Leeds defence and Matias flicked the ball from right foot to left, wrong-footing Liam Cooper, as he sent an immaculately-judged lob just under the bar in a classic smash-and-grab raid.
Wednesday defender Tom Lees was booked against his old club for shirt-pulling and Leeds almost equalised just before the break when Antenucci’s cross was chested just wide by Wood.
Despite abundant effort from both teams, it had been a largely untidy first half, with Mr Jones’ whistle rarely far from his lips.
Leeds were quicker out of the traps at the start of the second half and, after Liam Palmer had hurriedly conceded a corner, Sol Bamba headed Phillips’ flag-kick straight at keeper Lewis Price, who was again deputising for Kieren Westwood.
Phillips then rustled the side-netting with a free-kick awarded for a foul on Byram by Matias just outside the right corner of the penalty box.
Leeds made a double substitution in the 56th minute, Alex Mowatt and Luke Murphy replacing Byram and Phillips.
Mowatt’s first contribution was to send a speculative shot high over the bar as Leeds struggled to break down the Owls’ stubborn defence.
They were at last rewarded just after the hour mark when inspirational captain Bamba combined with Mowatt to send Dallas cutting in from the right and he rolled the ball into the goalmouth where Wood stretched to prod his second goal in as many games.
Both sides squandered gilt-edged chances within a minute. First Kieran Lee should have restored Wednesday’s lead in the 67th minute but after a swift build-up he headed weakly at Silvestri. Then Wood had most of the goal to aim at but contrived to nod the ball wide from eight yards.