Everton almost went back in front immediately when Bolasie set up Idrissa Gueye for what looked like a certain tap-in but Kelly got across to make a superb block.
The home side got the jitters after that and Delaney thought he had given Palace the lead – but after a long delay, the goal was ruled out.
EVERTON (4-3-3): Stekelenburg; Coleman, Jagielka, Williams, Oviedo; Cleverley, Barry, Gana; Bolasie, Lukaku, Barkley. Subs: Robles, Mirallas, Lennon, Valencia, Funes Mori, Davies, Holgate.
CRYSTAL PALACE (4-2-3-1): Mandanda; Ward, Tomkins, Delaney, Kelly; McArthur, Ledley; Townsend, Puncheon, Zaha; Benteke. Subs: Flamini, Cabaye, Campbell, Hennessey, Lee, Fryers, Wickham.
Referee: Jon Moss