Gary Johnson's men went into the game knowing that only a win would be good enough to keep their extremely slim hopes of avoiding a return to League One intact.
But late goals from substitute Kazenga LuaLua and Jesse Lingard sent them to defeat at the Amex Stadium and confirmed their fate.
Yeovil almost took a first-half lead when Ruben Palazuelos fired a 25-yard effort against the crossbar.
But as the tension increased, LuaLua came off the bench to give Brighton the breakthrough with 11 minutes left when his ball into the box evaded everyone and found the bottom corner.
That lead was doubled in injury time when Lingard converted Solly March's cut-back to leave Yeovil bottom and six points adrift of safety with just a game to play.
Victory for Brighton, meanwhile, moves Oscar Garcia's side above Reading, who visit Doncaster Rovers on Saturday, and into the play-off places.
Meanwhile, in League One, Sheffield United also left it late to beat Port Vale as they came from behind to register a 2-1 win.
Louis Dodds had put the hosts in front six minutes after the break but two late strikes in the space of the last seven minutes from Jamie Murphy and substitute Chris Porter turned the game on its head.
