Alan Quinn hit the first on 52 minutes with Gerald Sibon and on-loan Allan Johnston striking twice in three minutes.
Sloppy Wednesday were two goals down after just 19 minutes as Reading were given yards of space in the home area.
Nicky Forster had keeper Kevin Pressman scrambling down at the far post with a low strike before he broke the deadlock after nine minutes. Full-back Graeme Murty floated over a cross from the right flank and the unmarked Forster headed in from close range.
Pressman had to make a brave stop at Forster's feet before Reading grabbed a second goal ten minutes later. The Wednesday back four were static as Sammy Igoe picked out Martin Butler, who toe-poked the ball past the helpless Pressman from14 yards.
The struggling Hillsborough side were short of ideas and the hardworking Shefki Kuqi was short of support as he set off down the left wing before firing over the top from a tight angle.
James Harper drilled in a low strike from the edge of the area that was pushed away by the Wednesday keeper, while Dutchman Sibon offered Wednesday fans hope with a dipping shot from 25 yards, the ball skimming a foot wide of the target.
Derek Geary set up Wednesday in the 52nd minute, his deep cross was chested down by Kuqi to Quinn and the little midfielder finished in style, slamming the ball into the roof of the net from 12 yards.
Sibon snatched the equaliser 17 minutes later with a spectacular strike from 25 yards before Johnston coolly lobbed Marcus Hahnemann from the edge of the area with 19 minutes to go to seal a superb comeback.