Leeds began the brighter of the two sides and could have broken the deadlock in the ninth minute. On-loan striker Steve Morison found himself with time and space six yards from goal, but he failed to make a clean connection and the ball skidded wide of the target.
Rodolph Austin was next to try his luck for the home team, but on two occasions he fired over the crossbar from distance.
Having been made to defend for most of the half, visiting Wednesday managed to open the scoring with their first meaningful effort on goal in the 27th minute. Stephen Warnock and Paddy Kenny failed to clear the danger and Jermaine Johnson took advantage by lifting the ball over Kenny and into the net.
Should Wednesday hold on for all three points, it will mean that Leeds have lost five matches on the bounce.