Jason Puncheon's 23rd-minute strike gave the visitors an ideal start and set the tone for the rest of the game: The Toffees attacked a heavily populated final third, while Palace looked to counter.
The away side then doubled their lead just after the break, as Scott Dann's header blunted any half-time encouragement from Roberto Martinez.
The Toffees finally opened their account on the hour mark—as Steven Naismith found the net—but the away side once again proved clinical on the break, scoring on 73 minutes through Cameron Jerome.
Kevin Mirallas' late strike prompted a final onslaught, which Palace managed to repel.
Here's a look at some Everton-related talking points to emerge from this contest.