The Toffees cantered to a comfortable home victory which sustains their strong momentum and keeps the visiting side looking over its shoulder towards the relegation places.
Goals from Gareth Barry and Kevin Mirallas sealed a victory which kept the Merseysiders in the Champions League qualification places, moving above cross-town rival Liverpool, which travels to Stoke on Sunday.
Barry's powerful strike - his third since arriving on a season-long loan from Manchester City - sailed in from 25 yards midway through the first half, and Mirallas sealed his side's win with an exquisite free kick in the 59th minute.
Roberto Martinez's side produced an excellent team performance, demonstrating ruthlessness against an opponent which had claimed 1-1 draws on its last two trips to Goodison Park.
Everton – which presented new signing Aiden McGeady to fans before the match – recalled captain Phil Jagielka following his recovery from a hamstring injury, but was missing midfielder Ross Barkley (toe), while Leroy Fer returned from suspension for Norwich.
The home side started brightly, immediately settling into a quick tempo that forced Norwich back, and should have taken the lead in the 12th minute, only for Romelu Lukaku to head Mirallas' pinpoint cross wide from three yards.
A heavy first touch from Gary Hooper let Everton off at the other end, but the visiting side remained on the back foot and Javier Garrido was forced to clear a corner at the far post before both Mirallas and Leighton Baines missed the target.
A goal seemed inevitable and Barry produced a moment of genuine quality to break the deadlock in the 23rd minute, charging forward before unleashing a left-footed strike from 25 yards that hit the right side of the net and gave Norwich goalkeeper John Ruddy no chance.
Norwich's record signing, Ricky van Wolfswinkel, almost equalized with a curling 20-yard effort that was well saved by Tim Howard, while Leon Osman and Seamus Coleman shot over as Everton pressed for a second.
Howard was off his line quickly to deny Hooper on the stroke of halftime, but Norwich failed to improve after the break as Everton continued to pour forward.
After Jagielka and James McCarthy had wasted half chances, Mirallas provided the second goal with a stunning set piece that curled into the top-left corner from 20 yards.
Lukaku, who led the line superbly throughout, was denied by a diving Ruddy and then had a goal ruled out for offside, while a late Norwich revival was highlighted by a Robert Snodgrass header that hit the post.
Nathan Redmond, Bradley Johnson and Van Wolfswinkel also had attempts on goal, but Everton stood firm to complete a valuable win.