Wednesday survived a scare when Keiren Westwood suffered a nasty fall and had to undergo treatment. The goalkeeper went unworked for the remainder of the half, but his opposite number was soon picking the ball out of his net.
After notching his eighth of the season, the striker crossed for Tom Lees to direct a header at goal which was tipped over the crossbar as Leeds ensured that no more damage was done before half time.
Leeds were level on 57 minutes when Taylor scored his second of the season by smashing beyond Westwood after Luke Murphy's free kick had reached him inside the box.
Wednesday responded and passed up two half-chances as Maguire blazed high on the turn and Stevie May headed over from a corner.
However, they never truly wrestled the momentum back from United and the Whites completed their comeback on 72 minutes when Morison beat Westwood at the second attempt, after being released by Byram's pass.
It was Neil Redfearn's side who had the only opportunities to add to the scores in a final 15 minutes which they comfortably managed, but the Owls will have the last laugh as they will finish above their rivals in the Championship table.