The Eagles had claimed three-consecutive draws prior to what was, remarkably, their first game outside of London in nine matches in all competitions, and a positive start resulted in them gaining an early lead.
A routine delivery into the box saw Maxence Lacroix comfortably out-jump Abdoulaye Doucouré and Marc Guéhi reacted quickly to flick the ball in at the near-post with 10 minutes on the clock.
Everton initially responded well with Dominic Calvert-Lewin unable to make a firm connection on Dwight McNeil’s low cross.
But with Eberechi Eze providing a constant counter-attacking threat in what had developed into an end-to-end encounter, it was of no surprise to see Palace regain their composure.
Eddie Nketiah triggered a brief moment of chaos inside the Everton six-yard box when he arrowed a shot towards the top-corner.
James Tarkowski’s deflection sent the ball spinning high above his own goal, as the Toffees defence scrambled desperately to clear.
Palace’s dominance increased as the half progressed with the hosts living dangerously right up to the HT whistle.
After seeing their attacking threat diminish in the first-half, Everton provided an immediate response from the restart.
McNeil fired a stunning curling effort from 25-yards sailing into the net to spark what would be a remarkable turnaround.
Seven-minutes later, McNeil showed another glimpse of his quality to control Jack Harrion’s deep delivery with a deft touch, before unleashing an emphatic low finish to put the Toffees in front.
Everton have made an artform of losing from winning positions this season but boosted by the return of Jarrad Branthwaite, showed increased resilience as the visitors gained the ascendancy in the latter stages.
Daniel Muñoz’s cutback fell just behind Jean Mateta, with the striker poised at close range, as the hosts rode their luck.
The Toffees briefly quelled the pressure when Doucouré broke through, but Lacroix recovered to execute a well-timed challenge.
And amidst the mounting late tension at Goodison Park, Everton were able to maintain their composure to capture an elusive three-points that leaves Palace teetering above the relegation zone.
Flashscore Man of the Match: Dwight McNeil (Everton)
