Having battled hard against the Toffees for 86 minutes and seen Luka Milivojevic miss a penalty, late strikes by Dominic Calvert-Lewin and Cenk Tosun saw the home side snatch the win right at the death.
All the action from an eventful game are now available to watch on Palace TV, as well as post-match reaction from the returning Connor Wickham and Aaron Wan-Bissaka, as well as manager Roy Hodgson.
If you haven't registered yet, then sign up today for free and you get access to a host of exclusive video content, including these highlights and interviews with first-team stars.
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.