Pedro Obiang, provider for Carroll's goal, put the visitors ahead with a long-range strike in the 44th before Mark Noble's free kick was deflected off Steven Davies and into the net to condemn Southampton to a sixth defeat in seven league games.
The victory lifted West Ham, winners of six of their last nine league games, to ninth while out-of-form Southampton sit four points and four places below in 13th.
(Reporting By Tom Hayward; Editing by Brian Homewood)
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