Cole Palmer is the fourth player to score four goals for Chelsea in a single Premier League match, after Frank Lampard (2), Jimmy Floyd Hasselbaink and Gianluca Vialli
Palmer opened the scoring in the 13th minute by curling a beautiful strike into the bottom corner after nutmegging Everton defender Jarrad Branthwaite and playing a one-two with teammate Nicolas Jackson.
He doubled the lead five minutes later, heading in a rebound after a Jackson shot had been saved by Everton keeper Jordan Pickford.
And the 21-year-old completed his hat-trick midway through the first half in style after he intercepted a poor pass from Pickford before lobbing the England goalkeeper from 40 yards out.
Jackson then inflicted more doom on Everton just before the break by volleying in Marc Cucurella's cut-back, before Palmer added his fourth from the penalty spot in the 63rd minute.
And Chelsea scored a sixth in the 90th minute when substitute Alfie Gilchrist netted his first goal for the club from a tight angle.
Chelsea stretched their Premier League unbeaten run to eight matches and are three points off seventh-placed Manchester United, who currently sit in the Premier League's last European spot, having played one game fewer.
As for Everton, they were playing in their first match since receiving a two-point deduction for a second breach of Premier League financial rules. They stayed 16th, two points above the relegation zone.
-- Courtesy of BBC Sport