The Toffees opened the scoring in the 29th minute through Andros Townsend’s penalty after Allan had been brought down in the box.
Then Abdoulaye Doucoure put the gloss on the three points when he finished off a fine team move in the 77th minute.
Those were the key moments everyone watching will remember.
But we take a look at the events you might have missed
Doucoure’s Park End gesture
Abdoulaye Doucoure’s 77th-minute strike sent Goodison Park into raptures.
The Frenchman revelled in his goal with those who were sat in the Gwladys Street end. It was the reward he deserved for an action-packed, combative performance.
Doucoure’s clearly loving life in his second season as an Everton player and thriving under his new responsibilities handed to him by Rafa Benitez.
And the former Watford midfielder didn’t forget to enjoy the moment with the fans at the opposite side of the stadium.
After toasting his strike with those behind one goal, Doucoure then ran up towards the Park End, savouring it with those in the stand and geed them up to continue the vociferous atmosphere.
He did the same at the end of the encounter during the post-match celebrations.
It really was a quite brilliant moment.
Surprise tactic met by disapproval
Benitez isn’t someone who keeps up with the latest footballing trends.
After taking charge at Goodison, the in-vogue tactic of playing the ball out from the back when Everton have a goal kick has almost exclusively been eschewed.
His mantra has been about getting the ball up the pitch as quickly as possible and flooding the box with blue shirts.
That’s why it was a surprise when the Blues opted to deploy such a tactic in the first half.
Yerry Mina and Michael Keane dropped into the box to collect the ball for Jordan Pickford, which was met by disapproval by some sections of the crowd.
It was understandable why they reacted in such a way. Everton never looked like they’d convince and cut through Norwich’s press.
And those fears came true when the Canaries robbed possession deep in Toffees territory.
Luckily for the home side, Daniel Farke’s men wasted a good opportunity to equalise.
If you were naming your Premier League player of the season so far then Demarai Gray would simply have to be in the mix.
Bought for £1.7 million, his dazzling displays are a fundamental reason why Everton are on the same amount of points as Man City, Man Utd and Chelsea as things stand.
Watching him down the years, he’s always been a pacy, lively winger.
It was one bit of cleverness that maybe went unnoticed, though. In the 20th minute, the former Leicester wide man shimmied out of the way of a cross, allowing the ball to go through to Salomon Rondon in acres of space.
The striker would have been disappointed he didn’t make Norwich keeper Tim Krul work more with his shot at the back post.
But it was all about Gray’s awareness around him as he knew where a team-mate in a better position stood rather than taking it under control for himself.