Tom Cairney introduced himself to the Fulham fans with a fine strike just before half-time but Tomer Hemed's penalty in second-half stoppage time handed the home side a home defeat.
The former Blackburn man unleashed a powerful 20-yard drive into the top corner to cancel out Sam Baldock's opener.
The home side were penned back in the first half by the Seagulls and a defensive lapse allowed Hemed to slide the ball home to give the visitors the lead. But, before the break, Cairney curled the ball home to draw Fulham level.
The home side had the better of the second half but Matt Smith missed a golden opportunity to seal the win when his free header was straight at David Stockdale.
It was set to be the second draw of the season for Kit Symons' side but Shaun Hutchinson brought down Kazenga LuaLua in the area with Neil Swarbrick pointing to the spot. Hemed stepped up and broke Fulham hearts with the players' reaction suggesting they had been relegated, not lost the second league game of the campaign.
