City continued to control the opening minutes, with David Silva curling a free kick just high four minutes later, before Vincent Kompany planted a powerful header over the crossbar. West Ham remained a threat on the counter, however, with Kompany forced into a couple of early mistakes.
West Ham were ahead three minutes later, however, when Morgan Amalfitano turned home from close range following excellent work from Valencia on the wing.
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City responded with a series of attacks, but Adrian denied Silva, before Stewart Downing headed over the City crossbar down the other end.
West Ham had half-chances in the latter stages of the half, but could add to the scoring despite a stinging low effort from Valencia and clever free kick from Amalfitano.