The Hammers are currently top of the table with six points from their first two matches, while Palace are down in 14th, having collected one point from their opening two fixtures of the campaign.
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The visitors did soon settle into the match, though, and Liverpool were largely limited to long-range efforts as Lovren and Daniel Sturridge fired speculative shots well off target
Spurs continued to look the more likely in the opening half hour, with Andros Townsend firing in a dangerous-looking cross, while Federico Fazio headed wide and Danny Rose had a shot saved by Brad Guzan