Substitute Shane Long was the Reading hero after stepping off the bench to hit the winner.
Hot-shot Kevin Doyle had cancelled out Sean McAllister's opener seconds before the break.
Reading, with just one win in six games, were hoping to bounce back after a surprise 1-0 defeat to Nottingham Forest at the weekend but it never looked likely as the Sheffield side dominated in opening half.
But they almost came unstuck after a slick move started and finished by Leon Clarke.
The beefy striker fed Michael Gray, the midfielder threaded the ball to McAllister who played a probing pass into the area as Clarke ran through on goal with Adam Federici charging off his line to snatch the ball at his feet.
Defender Richard Wood squandered a half-chance after heading a Gray corner over the top, before Wednesday were caught on the break by ex-Sheffield United defender Chris Armstrong.
The Reading full-back cut inside from the left wing, darting between Lewis Buxton and Richard Wood, before hammering a low angled strike wide of the far post from 15 yards.
Reading recovered after a shaky start and almost broke the deadlock after winning a free-kick on the edge of the Wednesday box, but Stephen Hunt's teasing ball curled over Lee Grant before cannoning off the bar.
Full-back Liam Rosenior caused problems as he charged down the right flank with the Sheffield side caught out again.
His cross on the run beat the Wednesday back four but evaded Doyle and Noel Hunt as the pair waited to pounce.
Wednesday broke the deadlock in time added on when Marcus Tudgay's pass found Clarke six yards out and with his back to goal, he unselfishly slotted a short pass to the incoming McAllister, who hit the ball first time past the helpless Federici from 10 yards.
Jermaine Johnson out-paced Armstrong as Wednesday looked for a second, but the winger sliced his right-foot strike wide of the target as Federici came out to narrow the gap.
Rosenior was foiled by Grant before Reading were level 11 minutes after the break when Doyle coolly headed in Marek Matejovsky's corner at the far post.
But Long grabbed the winner in the 81st minute after charging in to slam Stephen Hunt's cross past Grant.
There was more drama in the dying seconds as the Wednesday keeper joined the attack and hammered in a low shot which was cleared off the line by Long.