A Wes Brown own goal 15 minutes from time was enough for the away side at the Stadium of Light.
Fulham are now just two points from safety, after beating the side directly above them – Norwich City – 1-0 at Craven Cottage; Hugo Rodallega the scorer.
Cardiff City have done their fight against the drop no harm with a 1-0 win at Southampton, Juan Cala the scorer.
Crystal Palace have edged closer to safety, and left Aston Villa in real trouble, with a 1-0 win over Paul Lambert's side at Selhurst Park, Jason Puncheon with the only goal of the game.
Tottenham have come from 3-0 down to draw 3-3 at West Brom – goals from Matej Vydra, Stephane Sessegnon and Chris Brunt had put the Baggies in charge, but a Jonas Olsson og, and goals from Harry Kane and Chrstian Eriksen levelled matters.
And Erik Pieters got the only goal of the game as Stoke beat Newcastle 1-0 at the Britannia.