The Hillsborough side were leading from a 55th minute Lee Peacock strike before the Brighton striker stabbed home a Sebastien Carole cross with seconds to go.
Wednesday should have had the game sewn up long before after carving out a hatful of chances and squandering the lot.
The Sheffield side had forced the early pace, Northern Ireland international Chris Brunt stabbing the ball to Peacock who produced a stinging shot from 15 yards that was pushed away in spectacular fashion by Wayne Henderson.
Brunt then carved out a half-chance finding space on the left flank before drilling the ball across the face of goal as David Graham failed to connect.
The Brighton goalkeeper blundered in the 18th minute though after charging off his line to clear as Wednesday probed for an opener. He slammed the ball straight to the lurking Chris Eagles.
The Manchester United youngster, on loan at Hillsborough until Christmas, miscued the ball straight to Graham who dragged his shot wide as Henderson raced back.
Brighton, pegged back for long periods, caught Wednesday on the break and almost stole the lead on 24 minutes. Carole saw a gap and produced a curling shot that was tipped round the far post by David Lucas.
Eagles, highly-rated by Sir Alex Ferguson, almost found a way through with a stinging drive, the ball flashing past the diving keeper and inches wide of the far post.
The hard-working Peacock had an effort blocked and as the ball ran loose to Brunt the 20-year-old fired in a low 22-yard shot that flashed wide of the target.
Wednesday broke the deadlock after Brunt surged from midfield to crack in a ferocious strike, Henderson found it too to handle and Peacock steamed in to finish off from 12 yards.
Peacock, Eagles and Brunt also threw away late chances to set up another nail-biting finish.