Reddy, on loan at Hillsborough until the end of the season, struck with virtually the last kick of the game to haul Wednesday off the bottom of the table and knock Portsmouth off top-spot for the first time since August.
The Irishman seized on Pompey defender Gianluca Festa's under hit free kick midway inside the home side's half before coolly slotting past helpless goalkeeper Shaka Hislop.
Portsmouth striker Lee Bradbury seemed to have set Harry Redknapp's side on their way into the top flight when he opened the scoring 20 minutes in.
Bradbury, playing his first game since returning from a two-month loan spell at Hillsborough, turned the ball home from four yards out after Owls goalkeeper Kevin Pressman could only parry Svetoslav Todorov's first-time shot.
Pompey out came all guns blazing after half time determined to send their fans home happy and had a number of chances to put the game beyond struggling Wednesday.
The visitors had the energetic Pressman to thank for keeping them in the game when he brilliantly blocked Bradbury's close-range shot just three minutes after the break.
Pressman was called into action again 20 minutes from time, turning Nigel Quashie's well struck shot after Todorov had broken free down the left.
Wednesday manager, Chris Turner threw on substitute's Reddy and Gary Holt 18 minutes from time in a desperate bid to keep his side's survival hopes alive.
That switch paid instant dividends as Owls defender Ashley Westwood almost immediately equalised with just 14 minutes remaining, side-footing his first goal of the campaign after Hislop had failed to clear a cross from the left.
Pompey threw everything forward in the closing stages desperate to regain the lead they had held for most of the match but it was Wednesday and Reddy, and not the 19,000 Blues fans who packed into Fratton Park who went home smiling.