The Seagulls have drawn 0-0 with Everton to move up one place to 15th on the table.
They now have 33 points, seven clear of 18th-placed Fulham.
Everton remain eighth, a point behind Tottenham Hotspur, but have a game in hand.
West Bromwich Albion earlier beat Southampton 3-0 in convincing fashion as Sam Allardyce's side look to salvage their top flight survival hopes in the home stretch of the season.
