Behrami's shot took a deflection off Sunderland striker Kenwyne Jones to beat stranded keeper Marton Fulop.
But on the stroke of half-time West Ham should have doubled their lead when Behrami missed a glorious chance.
West Ham could have levelled almost immediately when Behrami burst down the right and picked out Cole in the area.
The striker took a look up and saw an advancing Behrami, who smacked his shot off the bar from five yards out.
The hosts showed some late battling qualities and substitute Franco chipped in after Valon Behrami's threaded pass, but it was all too late.
That led to Grant replacing Radoslav Kovac with Obinna after 64 minutes, and Valon Behrami came on for Luis Boa Morte eight minutes later.
After a nervous opening, Valon Behrami released the growing tension 11 minutes before the interval by bundling home Frederic Piquionne's header inside the area.
He will take the place of Valon Behrami in the West Ham squad, as the Swiss international is close to securing a move to Fiorentina.
Behrami should have added a second but hit the bar from five yards out, while Sunderland striker Cisse was guilty of missing a number of chances.
Lars Jacobsen's cross was headed down by Piquionne and Behrami timed his arrival perfectly to score from close-range, to roars of elation and relief from the crowd.
West Ham midfielder Valon Behrami is the only other British-based player to feature for the Swiss, who will face tournament favourites Spain, Chile and Honduras in Group H in South Africa.
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The Black Cats failed to clear a free-kick and Behrami latched on to the loose ball to drive a shot from inside the box that deflected off Jones and into the net.
Valon Behrami shot just past the post and Bellamy blazed over after a neat knock down by Cole as the Hammers had their best spell at the end of the first half.
Yakin also missed an even easier chance than the goal he scored in the 34th minute when he stabbed the ball wide of the post following a superb right-wing cross by Valon Behrami which cut out the defense and goal custodian.
Denilson played a one-two with Bendtner and although there was a hint of a use of arm when getting past Valon Behrami, the Brazilian was soon dancing the samba after striking the ball low into the net for his sixth of the season.
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