Southampton work a corner short, Tadic lays it off for Davis, whose cross to the back post goes wide without threatening the West Ham goal.
Poor Fonte is having a shocker back on his old stomping ground, floating an aimless pass forward and well beyond the reach of his attacking team-mates to bring a promising period of play to a close for West Ham.
Fraser Forster can only parry it and Javier Hernandez, the poacher extraordinaire, is on hand to follow up and open his Premier League account for West Ham.
Davis, who has been pulling the strings for Southampton late in this half, gets to a loose ball ahead of Fonte and shoots wide from close range.
A rare spell of West Ham possession ends in a Southampton counterattack and the Saints are probing for a third, Nathan Redmond with a shot blocked on the edge of the Hammers' area there.
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