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Tomas Soucek, Michail Antonio and Nayef Aguerd scored for David Moyes’ men in the battle of London rivals.
Technical trouble at the turnstiles caused a 15-minute delay to kick-off but the end-to-end action at a sun-drenched Selhurst Park was well worth the wait with five goals in the first half alone.
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The win meant Palace leap-frogged Chelsea into 11th place in the table on 40 points after 34 games – two more than Chelsea have played. West Ham dropped to 15th, five points clear of the drop zone with five games remaining.