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The Saints took the lead in the 12th minute under bizarre circumstances as Black Cats defender Santiago Vergini diverted the ball past Vito Mannone into his own net as he tried to clear the ball inside his own box.
Southampton doubled their lead as they capitalised on further poor defending from the visitors when Will Buckley's pass hit the back of Sebastian Larsson. Steven Davis picked up the loose ball and teed up Graziano Pelle in the middle, who was left with a simple finish.
Gus Poyet's side almost got a goal back when Larsson curled a free kick over the wall from 25 yards out, but Fraser Forster was on hand to make a good save to beat the ball away from the net.
The home side took advantage of this decision as they scored their third goal of the game when Dusan Tadic beat the challenge of Vergini before finding Jack Cork in the area, who found the net with a neat finish.