After a superb turn inside the box, striker Dominic Calvert-Lewin tapped into the far corner to put the hosts ahead after 11 minutes.
After the break, Anthony Gordon tapped in a rebound to make it 2-0, though it was initially called out for offside before being correctly overturned by VAR, and substitute Dwight McNeil added a third late on.
Frank Lampard’s Everton started strongly and had numerous chances throughout, but Michael Olise came close for Palace in the second half.
Despite improving marginally in the second half, Palace, who have come from behind in all three of their Premier League triumphs this season, never really had a good foothold on the game.
Everton were outstanding, causing numerous issues in attack and displaying the ruthlessness Lampard has urged in recent weeks.
The Blues go up to 11th place, level on points with Palace, who drop to 12th.
It was also another step forward for Lampard as he seeks to rebuild Everton following their near-relegation last season, which they averted with a 3-2 victory over Palace in May.
In his pre-match programme notes, Lampard urged his team to display more “bravery” and a “clinical edge” in the box.
They were quick to assert their authority, pressing high and aggressively, forcing Palace into defensive errors and pushing them deep into their own half.
Amadou Onana was particularly impressive in midfield, effectively breaking up play and exchanging possession, while Gordon was active down the right side throughout.
Everton’s first goal came from that side of the field, as Calvert-Lewin placed pressure on Luka Milivojevic.
The Palace skipper lost possession and when Alex Iwobi fizzed it into Calvert-Lewin’s feet, he did the rest with a slick turn to beat Marc Guehi and capped it off with a composed finish in front of watching England boss Gareth Southgate.
Calvert Lewin’s opener was exactly what Lampard had hoped for, and he received a standing ovation when he was substituted later in the second half.
Everton were in command throughout, despite being irritated at times, and Iwobi’s backheel set up substitute McNeil to score from close range.