At Hillsborough, Harry Redknapp's men suffered their fifth defeat in the last eight games to leave them 10 points adrift of second-placed Burnley with 10 games to go - and destined to settle for a play-off place.
This miserable loss did not come without controversy, though, as Rangers were reduced to 10 men in the 35th minute when Richard Dunne fouled Leon Best. The contact was minimal and Best was unlikely to have control of the ball had he stayed on his feet, but the former Manchester City defender had to walk.
Chris Maguire converted the penalty and from then on it was all Wednesday, who under Stuart Gray are a team full of attacking intent and one undoubtedly on the up.
Best, who cleverly played for a foul in the penalty incident, provided a second six minutes after the restart with a fine finish after twisting and turning in the box and Lewis Buxton made it three from a corner in the 71st minute.
The Owls were rampant and could have easily bettered the four goals they got against Birmingham at the weekend had it not been for some wayward finishing.
It did not start off like that for Rangers, however, as they enjoyed a confident opening and should have led in the ninth minute. Joey Barton's free-kick found Clint Hill unmarked, who had stolen a march on the Wednesday defence, but the defender headed wide of the far post.
Things burst into life in the 35th minute with a moment of drama that changed the course of the game.
Best was set free down the Wednesday left and as he entered the box Dunne challenged him, with the on-loan Blackburn striker going down. Referee Paul Tierney pointed to the spot and dismissed Dunne, who protested his innocence.
Maguire calmly stroked the resulting penalty into the bottom corner as Rangers had the rug pulled from underneath them.
And they were fortunate to get into half-time with just the one-goal deficit as Maguire headed a great chance wide soon after and Brian Murphy made a superb save to deny Atdhe Nuhiu's powerful header, which may have crossed the line.
There was no respite after the restart, though, and Wednesday doubled their lead with a fine goal. Defender Oguchi Onyewu embarked on a marauding run out of defence and fed Best, who superbly turned his marker and fired a low effort past Murphy.
It was damage limitation for Rangers and Wednesday could have had any number as they controlled the final 30 minutes.
Maguire skewed an effort wide and Nuhiu, in possibly his best game for the Owls, volleyed over, but there was no denying them in the 71st minute.
A corner was not cleared properly and Buxton slammed home a 16-yard effort across goal to make it seven Wednesday goals in two matches.