This was an excellent win against a Magpies team very much on the up and enjoying a fine campaign so far.
The Toffees also scored three goals at home for only the second time this season to match the scoreline in their previously solitary home win against Bournemouth.
It was also a result that underlined the huge progress that the Blues have been making this season, something that previous results had often not highlighted, especially at Goodison Park.
Furthermore, the result represented a second straight victory without conceding a goal, following the points deduction and after that initial defeat to Manchester United.
Had Everton not been given that absurd and totally unjustified punishment - unprecedented in English football history - the club would now be comfortably sitting in mid-table and looking upwards towards the European places.
A win tonight also represented a statement that this team can produce both a decent performance against a good side (albeit one with a lot of injuries) and crucially score goals at the Grand Old Lady.
Too many times of course this season the Toffees have created chances and spurned them only to regret that wastfulness with earlier home defeats to Fulham, Wolves and Luton Town proving particularly damaging.
And it looked as though the same storyline was unfolding tonight as Everton once again couldn't take the first half opportunties that they manufactured.
Dominic Calvert-Lewin was most guilty, wasting several great chances including one when he was alone in front of goal and blasted the ball over just yards out.
To be honest I am a little concerned at his recent poor form in front of goal. While the all-round game is still strong, he hasn't scored since netting against West Ham at the end of October.
Newcastle had their opportunities too and it had been quite an open and very competitive match which was still somehow 0-0 at halftime.
In the second half things continued in a similar vein with a back and forth but fewer clear-cut chances and the biggest scare for the home side was when Jordan Pickford looked to have an injury that might force him off.
As it was he stayed on the pitch, and had again underlined his importance earlier with a couple of good saves to keep the scoreline level.
Then as the game looked like it was running out of steam and heading for a goalless draw, Everton scored three times late on to take the points.
First Dwight McNeil netted for his second goal in the last two matches following his winner at Nottingham Forest last weekend.
Abdoulaye Doucoure then popped up to add a second, unusually for him scoring at Goodison, as he generally gets his goals away from home.
Finally, substitute striker Beto ran on to calmly slot home for his first ever Premier League goal sealing a great win and a very valuable three points.
The coming few weeks are going to be important of course with a slew of games to be played over the festive period, as usual.
So far in December Everton have maximum points from their first two matches. Can they now reproduce this sort of effort against Chelsea on Sunday and keep a perfect record so far this month?