The Toffees have hit the ground running in the last fortnight, and first half goals from Dominic Calvert-Lewin and Richarlison secured a third straight win for them.
The visitors were quickest out of the blocks in south London, as the razor-sharp Calvert Lewin nodded home Seamus Coleman’s cross after 10 minutes.
However, despite the early setback, Palace refused to panic, and makeshift centre back Cheikhou Kouyate powered them level on 26 minutes.
Both sides created a flurry of chances before the break, but it was Everton who edged back in front, amid more VAR controversy.
Referee Kevin Friend check and double checked a handball against Joel Ward, but despite the contact looking minimal against the Palace full back, Richarlison grabbed the opportunity to tuck home from the spot.
The Blues looked to push home their advantage after the break, but the on-form Calvert-Lewin wasted two excellent chances to put the game to bed.
Kouyate missed Palace’s best chance to equalise late on, but the visitors showed their experience in the closing stages to seal another three points for Ancelotti.
FULL TIME AT SELHURST PARK IT’S CRYSTAL PALACE 1 EVERTON 2