Marcelo Bielsa' s men gave a lacklustre display in Liverpool on Saturday as Frank Lampard claimed his first victory as Everton manager.
The Whites travelled to Merseyside hopeful of putting further daylight between themselves and the dreaded drop zone.
Everton, who hadn't won a league game since December, flew out of the traps and enjoyed all of the early chances.
Disaster struck for the visiting side when Stuart Dallas, following a coming-together with Blues winger Alex Iwobi, was forced off in the eighth minute to be replaced by young defender Leo Hjelde.
Minutes later, the hosts took the lead through Seamus Coleman and Leeds struggled to get a grip on the game.
Michael Keane doubled Everton's lead in the 23rd minute, rising higher than Robin Koch and Pascal Struijk to thump a header past Illan Meslier from a corner.
Bielsa used his remaining subs to pull Raphinha and Mateusz Klich off at the break, replacing them with Adam Forshaw and Tyler Roberts.
The new players did little to change Leeds' fortunes, though. Richarlison's 78th-minute deflected strike added further misery on a sorry afternoon in Liverpool.
The game ended 3-0, with the Whites failing to register a single shot on target across the 90 minutes.
2. Everton v Leeds United
The players survey the pitch at Goodison Park. Photo: Bruce Rollinson
3. Everton v Leeds United
Illan Meslier and Pascal Struijk chat before kick-off. Photo: Bruce Rollinson
5. Everton v Leeds United
Raphinha and Anthony Gordon race for the ball. Photo: Bruce Rollinson
6. Everton v Leeds United
Seamus Coleman opens the scoring for Everton. Photo: Bruce Rollinson