Matty Fryatt, making his debut in a month-long loan deal from Hull, had fired Wednesday into a first-half lead, before Andrews hit a last-gasp equaliser from six yards.
Under-fire Owls boss Dave Jones has remained upbeat about his team's start to the season - despite overseeing their worst start to a campaign since 1999.
But Wednesday remain without a win this season and have collected just five points from nine Sky Bet Championship outings.
David Lopez had fluffed an early opening for the home side with only goalkeeper Chris Kirkland to beat after being set up by Bruno Saltor.
Kirkland was again called into action after Argentinian striker Leo Ulloa, returning from a three-game ban following his red card in Brighton's goalless draw with Reading, was put through by Inigo Calderon.
Wednesday had endured consecutive defeats in their previous two Championship outings at Birmingham and Doncaster, but went ahead in the 43nd minute against the run of play after surviving a steady stream of first-half pressure from the home side.
Jeremy Helan found possession inside the box and picked out Fryatt, who turned and drilled a low shot past Tomasz Kuszczak from six yards - his first goal since April 2012.
Brighton had two first half penalty appeals turned down - Kazenga LuaLua went down inside the box under pressure from right-back Lewis Buxton, and Andrews fell to the ground after an off-the-ball incident with Jose Semedo.
The Seagulls had collected seven points from their previous three home matches following an opening-day defeat at the Amex to Derby, but went in behind at half-time just as they had against Bolton 10 days earlier.
The introduction of winger Will Buckley after the break added pace to a Brighton team lacking in a killer-instinct, but clear-cut chances were still a rarity.
Striker Ulloa was carried off on a stretcher 10 minutes into the second half as Brighton, deprived of a cutting-edge, resorted to hit-and-hope attempts.
Midfielder Andrews hit a 20-yard volley which whistled past Kirkland's post and LuaLua attempted a long-range drive as Oscar Garcia's men searched for a leveller.
Substitute Jermaine Johnson then went close to doubling Wednesday's lead after darting into the box and firing a low-left foot shot at Kuszczak in the 80th minute.
Then, with time running out, defender Stephen Ward headed the ball back across goal after slack Wednesday defending, and Andrews pounced to rescue a last-minute point for Garcia's men.
Michail Antonio almost won it for the away side in stoppage-time but produced a tame shot when one-on-one with Kuszczak.