Crystal Palace took control from the first whistle and were quickly rewarded when Marc Guehi opened the scoring in the 10th minute, poking home the first shot of the game with a true striker's finish at the near post.
The goal appeared to spark the game into life, with both teams creating numerous goalscoring chances in the following 35 minutes, but the score ultimately stayed the same as Crystal Palace held their lead heading into the break.
It was Everton who started stronger in the second half, and it took them just two minutes to level the score as McNeil hit a wondrous curled strike into the top left corner.
The hosts maintained their momentum right after their goal, with McNeil scoring again just seven minutes later to put Everton in the lead, volleying home from inside the area after a composed touch set up the shot perfectly.
The visitors grew into the game heading into the final moments, applying plenty of pressure on the Everton defence in search of an equaliser, but the Toffees stood strong and took all three points.
EVERTON VS. CRYSTAL PALACE HIGHLIGHTS
Marc Guehi goal vs. Everton (10th min, Everton 0-1 Crystal Palace)
Crystal Palace have taken the lead in the Premier League for the first time this season!
Adam Wharton loops a high cross towards the back post, where Maxence Lacroix climbs above Abdoulaye Doucoure and is able to head the ball down towards goal.
Marc Guehi finds himself in the perfect position and expertly flicks the ball past Jordan Pickford with the outside of his boot, giving Crystal Palace an early lead with their first attempt on goal.
Dwight McNeil goal vs. Crystal Palace (47th min, Everton 1-1 Crystal Palace)
What a strike from McNeil to bring Everton level!
Ashley Young wins the ball back and plays a disguised pass to McNeil, who takes a touch and finds himself in plenty of space outside the Palace penalty area.
McNeil opens up his body and hits a stunning curled effort past Dean Henderson and into the far left corner, equalising with Everton's first shot on target of the match.
Dwight McNeil goal vs. Crystal Palace (54th min, Everton 2-1 Crystal Palace)
Absolute magic from McNeil to quickly turn the game in Everton's favour.
A long free-kick is sent forward by Pickford, with the clearance being brought down beautifully by Jack Harrison, who turns and delivers an inviting cross towards the back post.
McNeil shows excellent composure as he takes a touch to set up a volley, striking the ball off the ground and past Henderson to complete Everton's turnaround.
MAN OF THE MATCH - DWIGHT MCNEIL
McNeil may have had a quieter first 45 minutes as the hosts struggled to get a foothold in the game, but Everton's number seven was simply sensational in the second half.
His two goals enabled the Toffees to complete a remarkable seven-minute turnaround after falling behind 1-0 early on in the game, helping to secure Everton's first three points of the campaign.
Guehi deserves an honourable mention for his performance, not only scoring for Crystal Palace but also delivering a strong defensive display that included 10 clearances, two blocked shots, one interception, and two tackles.
EVERTON VS. CRYSTAL PALACE MATCH STATS
Possession: Everton 40%-60% Crystal Palace
Shots: Everton 8-16 Crystal Palace
Shots on target: Everton 2-5 Crystal Palace
Corners: Everton 5-8 Crystal Palace
Fouls: Everton 12-11 Crystal Palace
WHAT NEXT?
Everton's 2-1 win saw them secure their first victory of the 2024-25 Premier League campaign, and they will look to make it two on the bounce when they face Newcastle United next Saturday.
Crystal Palace remain in search of their first league win of the season after the defeat to the Toffees, and they will aim to achieve it against another Merseyside club when they host Liverpool next weekend.