Goals early in each half from Richarlison and Dominic Calvert-Lewin put the home side 2-0 up and although Mateo Kovacic pulled one back, Calvert-Lewin struck again late to seal the win.
The three points for Everton, under the temporary charge of Duncan Ferguson following the sacking of Marco Silva, lifts them to the relative comfort of 14th spot in the table.
Frank Lampard’s men remain in fourth place but Wolves could close the gap to just three points if they beat Brighton on Sunday.
Ferguson’s reign at Goodison Park got off to the perfect start with Brazil forward Richarlison heading home Djibril Sidibe’s cross from the right to give the hosts a fifth-minute lead.
Chelsea pushed for an equaliser, with in-form England forward Tammy Abraham going close a couple of times, but the Toffees went in at half-time 1-0 up.
Everton got a flying start to the second half as well, with Calvert-Lewin barging his way through the Chelsea defence before slotting past Kepa Arrizabalaga from 12 yards.
But Chelsea responded immediately, with Kovacic stroking in a volley with his right foot in the 52nd minute, beating the dive of England goalkeeper Jordan Pickford.
The visitors continued to dominate possession but Everton looked dangerous on the break, with Theo Walcott seeing a shot parried at the near post.
Substitute Tom Davies mistimed a header when in a good position to restore Everton’s two-goal lead.
But Chelsea shot themselves in the foot when Kepa mishit a pass, gifting possession to Walcott.
The ball came to Davies, who struggled to control the ball, but it eventually fell for Calvert-Lewin, who bundled home, sending Ferguson charging down the touchline.
Victory is a huge boost for Everton, who slumped to a 5-2 defeat against Liverpool in midweek. They have a tough run of fixtures coming up including both Manchester clubs away from home.
Lampard’s young team won six successive Premier League games to climb into third place in the table last month but have since stumbled, losing to Manchester City, West Ham and now struggling Everton.
The manager will now turn his attention to Tuesday’s Champions League match at home to Lille. They will qualify for the knockout stages if they beat Lille or if they draw and Valencia lose to Ajax.
Chelsea were buoyed by the decision of the Court of Arbitration for Sport on Friday to reduce their FIFA-imposed transfer ban, meaning they can sign players in the January window.
Lampard welcomed the outcome but said the club would have to be careful with their recruitment policy after a fine start to the season with a crop of young players.