Valon Behrami's first West Ham goal ended their search for a Barclays Premier League victory at the eighth attempt as Sunderland were once again made to pay for missed chances.
The Switzerland international struck after 20 minutes and then passed up a glorious opportunity to make it 2-0 when he hit the bar from six yards in first-half injury time.
Roy Keane's side dominated for long periods, but were unable to make the most of their possession with striker Djibril Cisse in particular guilty of a series of misses.
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