The Eagles opened the scoring in a dominant attacking period as Christian Benteke slammed home a header - the Belgian frontman appearing in-form and confident.
Roy Hodgson's men then enjoyed several exciting chances but couldn't add to their tally before half-time.
They emerged for the second-half with the wind in their sails but were soon undone by Sebastien Haller's sensational bicycle kick, which inspired West Ham back into the game.
The Eagles' task finally became too much to handle when Benteke received a harsh second yellow card, and the south Londoners were forced to defend a point rather than hunt down two more.
To watch both goals, every eye-catching Palace attack and pore over the sending off, head over to Palace TV by clicking here or 'Palace TV' within the app for full match highlights and reaction.
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