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The home side had a good chance for an early goal, Junior Hoilett creating some space before firing his shot just wide.
The Canadian spurned another effort inside a strong opening 10 minutes for QPR, but the finish was off-target again, smashing the ball wide of the post.
Despite the hosts' early chances, it was Sunderland that broke the deadlock, Fletcher scoring his first goal in five games, tapping the ball in from close range.
Remy had two chances to give Harry Redknapp's side the lead late in the first half, but a save from Mignolet and a high volley prevented the Frenchman from securing his second goal of the game.