Daniel Munoz skipped a weak effort straight at Pickford before Chilwell latched on to a long ball from Wharton and induced a dive from the Everton keeper, though his effort's trajectory looked wide of the target.
The Eagles failed to clear the ball from inside their penalty area, where the rebound from 79th-minute substitute Ashley Young's cross off the chest of Will Hughes bounced favourably in the path of Alcaraz, who opened his Everton account with a low finish.
Lerma had the ball in the back of the net moments later, but a VAR check determined Devenny's corner had drifted out of play before the Colombian nodded it in.
It began with a Palace corner that was only half-cleared and kept alive by Wharton before Mateta was set up by Guehi with a neat overhead flick for the Frenchman to finish from six yards out.
The newly invigorated hosts threatened before Henderson denied Beto a second and Glasner swapped Mitchell for Chelsea loanee Ben Chilwell, making his first Premier League appearance in an Eagles shirt.
