Hazard put Chelsea ahead with a low, angled shot, before Marcos Alonso added a second when he slotted through Maarten Stekelenburg's legs.
Diego Costa made it 3-0 just before half-time, and Hazard scored the pick of the goals after the break.
Pedro put the gloss on the result when he tapped into an empty net.
Everton spent the majority of the game penned in their own half and did not manage a shot on target in the entire 90 minutes as Chelsea produced a ruthless and dominant performance.