Goals either side of half-time from Ross Wallace and Kieran Lee will see Wednesday - who finished the regular season 15 points adrift of their opponents - take a 2-0 lead into the second leg on the south coast.
Hughton's side, who came within one goal of going up at Middlesbrough last weekend, lost no fewer than four players through injury and were forced to play the last half-hour with 10 men having used all their substitutes.
Tomed Hemed, Connor Goldson, Steve Sidwell and Anthony Knockaert will now all face fights to be fit for the second leg - while Wednesday will travel south confident of moving within one match of a place in the Premier League.
Brighton had already been forced to line up without Dale Stephens, whose sending off shortly after scoring at the Riverside effectively ended their hopes of claiming the three points they needed to avoid the end-of-season lottery.
So it was no real surprise that Wednesday started brightest, with Wallace immediately posing a threat going forward and firing an early warning shot over the bar.
But the Seagulls soon got a grip and began exploiting gaps behind the Wednesday defence, Hemed crossing for Sam Baldock whose seemingly goal-bound effort was deflected behind after eight minutes.
From Jiri Skalak's resulting corner, Brighton came desperately close to taking the lead when Hemed's header hit the bottom of Wednesday goalkeeper Keiren Westwood's left-hand post.
Wallace flashed another effort inches wide at the other end before the game erupted in controversy in the 19th minute when Fernando Forestieri chased down a long ball from keeper Westwood and slotted past David Stockdale.
Despite extensive celebrations, referee Andre Marriner consulted with an assistant and eventually disallowed the goal on the basis that the striker had been offside when Westwood had launched the ball forward.
Furious Wednesday boss Carlos Carvalhal made his displeasure clear from the touchline and the incident led to a frustrating and fractious period which was drawn out by the successive injuries to Hemed and Goldson which resulted in both being substituted.
Wednesday finally made their breakthrough in the last minute of the first half when Wallace picked up a neat ball from Gary Hooper on the right and drifted inside before drilling a low shot past Stockdale.
Daniel Pudil lashed an effort wide for Wednesday early in the second half before Brighton's bad luck continued with Sidwell becoming the third visiting player to be replaced after pulling up.
Just before the hour-mark it went from bad to worse as Knockaert stretched for a long ball into the Wednesday box and was subsequently carried off on a stretcher, with Hughton having no option but to re-structure with 10 men.
Skalak curled a free-kick just over the bar for the visitors before Wednesday doubled their lead in the 73rd minute, Forestieri threading the ball into the box for Lee to fire calmly past Stockdale and ignite Hillsborough in celebration.
Wednesday had a penalty appeal turned down when Richie Towell brought down Forestieri in the box, and Skalak came close late on for Brighton as a dismal night for the visitors ended without any reward.