The Eagles slipped to a third successive defeat thanks to Danny Ings' goal a minute after half-time, and then Mark Hughes' team clinched the win in stoppage-time when Pierre-Emile Hojbjerg tucked home a goal on the counter-attack.
Between those moments, Palace were given a glimmer of hope when Wayne Hennessey made his first penalty save for the club to deny Charlie Austin, and they also hit the crossbar through James McArthur and forced ex-Eagles keeper Alex McCarthy into plenty of saves, but it just wasn't to be their day.
All the action is now available to watch on Palace TV, as well as post-match reaction from Wayne Hennessey and manager Roy Hodgson.
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Head to Palace TV now to watch all this great content free of charge, or register with the service, or if you are on the official club app, simply head to Palace TV and go into the Video channel.