Dwight McNeil broke the deadlock in the final 15 minutes after dispossessing Kieran Trippier deep in his own half before unleashing a powerful strike.
A second followed for the Blues barely ten minutes later as McNeil dummied a Jack Harrison pass for Abdoulaye Doucoure, who rifled the ball home.
Deep into stoppage time, substitute Beto added a third with a superb run and finish in front of the Gwladys Street End for his first Premier League goal.
Sean Dyche’s side now sit a point outside the top flight’s bottom three places, having clawed back their 10-point deduction in the space of just three weeks..
Here were the key talking points from Goodison Park:
Dyche’s men shall not be moved
From the moment Everton were hit with a Premier League record 10-point deduction three weeks ago, one mantra has become resoundingly clear.
The biggest sporting sanction in top-flight history demanded an equally emphatic response and the Goodison faithful certainly delivered it.
Since that excessive punishment was handed down last month, the once-ritual chant of ‘We shall not be moved’ has developed a new lease of life.
What previously soundtracked the Blues’ trophy-winning heyday is now becoming synonymous with the club’s resurgence under Sean Dyche.
But not even the most optimistic Evertonian could have foreseen their team putting a high-flying Newcastle United to the sword in such emphatic fashion.
It was a victory which secured their escape from the relegation zone and bore testament to the strides Dyche has undertaken in spite of punitive measures.
Finally, they can again start to look up the table instead of just the periphery.
Roles reversed in floodlit trilogy
One way or another, a third Thursday outing with the Magpies in successive Premier League seasons promised to be another memorable occasion.
Last April’s showdown became notable for very different reasons as Everton’s first-half command descended into a total onslaught following the interval.
History threatened to repeat itself after an opening 20 minutes where the hosts had 19 touches in the opposition box compared to Newcastle’s sole attempt.
Role reversal, however, was exclusive to Dyche’s men continuing to ramp up their ascendancy and see it handsomely rewarded in the game’s final quarter.
Their relentless pressing saw Kieran Trippier easily dispossessed Dwight McNeil’s smash-and-grab opener; bearing down on goal with relative ease.
Defensively, too, there was no repeat of the wilful surrender that saw gifted Eddie Howe’s side three goals in nine second-half minutes last time out.
Repeated chants of ‘ole!’ in added time further illustrated how comfortable nature the Grand Old Lady’s latest floodlit trilogy instalment had become.
Gordon eats humble pie on return
On the visitors’ last visit to Goodison, Anthony Gordon refused to hold back.
Mere months after securing an eight-figure transfer to the North East, the Kirkdale native revelled in getting one over on the club that had nurtured him.
Footage of Gordon exuberantly fist-pumping his way back to the dressing room left a sour taste while his former employers were scrapping for survival.
Little wonder, then, that his every touch was greeted with ear-splitting disdain from Everton supporters situated on all four sides of this famous old stadium.
Not that Gordon had much joy on his old stomping ground thanks to several of his ex-teammates ensuring a largely subdued second return to Merseyside.
When he did manage to find a way through the backline in the second half, the self-styled ‘Starboy’ was already blindsided by the potential headlines.
Gordon’s development since leaving Everton is undeniable but he was left choking on humble pie long before fans rhetorically asked, ‘What’s the score?’
