An early own goal by Brighton's Gary Hart and a second-half solo effort by midfielder Burton O'Brien ended Wednesday's woes and sentenced Brighton to League One after two seasons in the Championship.
Brighton, needing to win to keep their hopes alive, started brightly before suffering a setback in the eighth minute.
Deon Burton got the better of Guy Butters and his low cross was turned into his own net by Hart from close range.
The goal knocked the stuffing out of the home side and it was not until the closing stages of the first half that they threatened an equaliser.
A header by Dean Hammond from a Richard Carpenter corner was hooked off the line by John Hills and Wednesday then survived a double escape on the stroke of half-time.
Keeper Scott Carson, on loan from Liverpool, saved a Paul Reid shot and Hammond's follow up was blocked by Owls captain Graham Coughlan.
Brighton brought on Alexandre Frutos and Sebastien Carole in the early stages of the second half and Colin Kazim-Richards went close to equalising with a 25-yard drive just wide.
But O'Brien killed the home team off in the 69th minute with a fine individual goal.
Collecting a pass from Burton, he made progress into the penalty area, rounded Hart and keeper Wayne Henderson and stroked the ball into the empty net.
Brighton's misery was completed by a red card for Hammond with nine minutes left.
The midfielder had already been booked by referee Paul Taylor for a foul in the first half on Glenn Whelan when he fouled the same player again.
Hammond's second dismissal of the season means he will miss Brighton's last two matches away to Wolves and at home to Stoke.