Callum Wilson scored a second half brace to lift enormous pressure off the shoulders of Newcastle boss Steve Bruce.
The win moves the Magpies up to 16th in the table, giving them their first league points of 2021 - ending a six game winless run in the Premier League.
There'll be huge frustrations for Carlo Ancelotti as a win would've moved his side back into a healthy position in their pursuit of bringing European football back to Goodison Park next season.
Story of the match
There was very little between the two sides in the opening half at a rather bleak Goodison Park. Newcastle, who came into the game off the back of a rotten winless run, started off as the superior of the two sides.
It didn't take long for Everton to find their groove, as ex- Real Madrid 'Galactico' James Rodriguez seemed to have awoken for this crisp Saturday afternoon encounter.
James supplied the Toffees with the opening chance of the game after a well worked free kick routine provided the Columbian with the time and space to architect a wonderful cross, which was met by the head of the incoming Yerry Mina. Although the defender should've done better with his effort, as he was unable to keep it below the bar.
Bruce set his side up with what seemed like a 4-1-4-1 formation. With Newcastle under the strains of Everton pressure early on, the outlets of Miguel Almirón and Ryan Fraser provided the Magpies with a dangerous option whenever possession was overturned. Everton received their first warning of the game early on, after a quick Newcastle break resulted in half chance for their star man, Wilson, who's shot from the edge of the box was deflected behind for corner.
There were plenty of encouraging signs for Bruce's me early on. Their play certainly didn't resemble a side that's failed to win a Premier League game since December.
The best efforts of the first half for both sides came just after the 20 minute mark. Richarlison was first up, after he dipped and weaved past two lime green shirts before letting-fly from just outside the box, where he shot was comfortable parried away by Karl Darlow.
At the other end it was Jordan Pickford's turn to keep it at a stalemate, the top of his finger tip is what came stopped Wilson from opening the scoring, after a fantastic header from Fraiser's corner.
If the first half was anything to go by, there was never going to be a goal fest after the interval.
As the clock ticked, each passing second seemed to amplify the pressure on Ancelotti's men. Frustration grew as the Magpies defence held strong, this was an opportunity Everton couldn't afford to let pass if their ambitions of qualifying for Europe next season were serious.
And pass them by it did. With just over 15 minuets left on the clock Newcastle's star man, Wilson, rose highest to flick home Jonjo Shelvey's corner into the far corner. Elation for the Magpies as the deadlock was broken.
Bruce allowed himself to crack a smile, after weeks of scrutiny, hostility and disapproval from all angles, Newcastle were finally on track to pick up their first three points of the new year, at the seventh attempt.
Wilson should've wrapped up the points with three minuets left on the clock after Almiron's perfectly weighted ball sent him one-on-one with the Everton 'keeper. He kept his cool as side-stepped past Pickford before smashing his effort against the post. Giving the Toffee's a lifeline, if they were to rescue anything from the contest.
There would be a final opportunity to secure the points deep into stoppage time when Newcastle broke clear after Everton sent almost everyone up for a corner.
As the resulting corner was cleared away Allan Saint-Maximin sent Jamal Lewis running down the left as the counter attack broke. Lewis, picked out Wilson, who was left unmarked in the centre, leaving him the time and space to prepare his finish before coolly slotting it past a helpless Pickford from just inside the box, sending Newcastle home with a rare three points on the road.
Everton: Pickford, Coleman, Keane, Mina, Digne, Doucoure, Iwobi, Sigurdsson, James, Richarlison, Calvert-Lewin
Newcastle: Darlow, Manquillo, Schar, Lascelles, Lewis, Hayden, Shelvey, Hendrick, Almiron, Fraser, Wilson