Albion are still seven points clear of the Premier League relegation zone - after West Ham gave the rest of the teams in the bottom half of the table a fright.
Next-to-bottom Hammers were ahead at half-time at Manchester City before eventually losing 2-1 to Pep Guardiola's leaders.
Angelo Ogbonna headed David Moyes' visitors into an improbable lead at the Etihad just before the break.
Nicolas Otamendi pulled City level early in the second half, the central defender's fourth goal in 14 appearances.
David Silva stretched to volley in the winner from Kevin De Bruyne's cross with seven minutes left, securing City's 13th win in succession.
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