The Eagles pulled themselves level through Patrick van Aanholt, who stepped-up to fill in the shoes of Luka Milivojevic and bury from the spot.
At the back, Vicente Guaita made a handful of impressive point-blank saves and Gary Cahill led the team as captain for the first time.
But the whole team seemed confident from kick-off, with Wilfried Zaha pinning the Hammers' defence back on occasions and James McArthur performing with strength.
Joel Ward celebrated his 200th league appearance in red and blue and enjoyed a performance that saw him attack and put his body on the line on several occasions.
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