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Agbonlahor was in the mix of things again as he was found by Andreas Weimann just outside the box, though the striker's long-range effort was kept out.
Sunderland looked to hit back with an effort of their own when Andrea Dossena let fly, only to see his shot creep just wide of goal.
Christian Benteke was presented with a great opportunity in the 29th minute, but the Belgium striker blazed his effort over with only the keeper in his path.
Sebastian Larsson threatened for Sunderland just before half time as he smashed a right-footed shot across the face of goal, with the ball creeping just wide of the far post.
Sunderland should have gone 1-0 ahead five minutes before the interval, but Emanuele Giaccherini somehow managed to put the ball over the bar with the goal gaping only a yard or so in front of him.