Roberto Martinez's men cantered to a comfortable home victory which sustains their strong momentum and keeps the visitors looking over their shoulder towards the relegation places
Goals from Gareth Barry and Kevin Mirallas sealed a victory which kept moved the Merseysiders into the Champions League qualification places, overtaking cross-town rivals Liverpool, who travel 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 ensured 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 opponents who had claimed 1-1 draws on their last two trips to Goodison Park.
Everton – who presented new signing Aiden McGeady to fans before the match – recalled captain Phil Jagielka following his recovery from a hamstring injury but were missing midfielder Ross Barkley (toe), while Leroy Fer returned from suspension for Norwich.
The hosts 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 visitors 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 with efforts.
A goal for the hosts 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 gave Norwich goalkeeper John Ruddy no chance of intercepting its route towards the right-hand side of the net.
Norwich's record signing, Ricky van Wolfswinkel, almost equalised 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 half-time, 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 was bent 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.