With six games to play the Magpies find themselves two points clear of fourth place Manchester United and crucially eight points clear of Spurs and Aston Villa and nine points clear of Liverpool.
However, a cautious Eddie Howe speaking immediately after the game said that they are taking nothing for granted, despite having a top-four finish all but secured.
"It puts us in a lot stronger position. To get six points from Tottenham and Everton is a great return”.
"It was always going to be a difficult game for us, but we handled the occasion well in a hostile environment”.
"The first goal was going to be crucial. It was probably our best move, and it came at a good time for us”.
"The confidence was there, and it was evident in the second half. Maybe a bit of the edge of the game had gone, but I think we had to earn the right to get to that point because Everton put us under pressure in the first half”.
"We know nothing is taken for granted from our perspective."
But behind Howe’s comments sit an air of confidence among supporters not seen around Tyneside for many years. And rightly so.
After a dip in form leading up to their Carabao Cup Final appearance Newcastle have picked up maximum seven out of the last nine league games scoring 23 goals with 10 goals coming in their last two games.
And in doing so they have shaken off the tag of draw specialists.
Having conceded only 26 goals this season Newcastle sit holding the title of meanest defence in the league and while their defence has proved to be Howe’s bedrock in his teams rise; the squad are adding goals-a-plenty and in doing so converting those draws to wins.
The return to form after illness and injury of striker Callum Wilson has been one of the main drivers and in Alexander Isak, they now have an additional striker with more than an eye for goal.
Between them they have 23 goals this season with Wilson currently shading it on 13 goals to Isak’s 11.
Howe chose to rest Isak; with him taking up a seat on the bench and it was Wilson in the 35th minute who got the opening goal of the game; somewhat against the run of play, as Newcastle stuttered to get any fluency into their game.
And it wasn’t until Joelinton's header in the 72nd minute allowed the travelling 3,200 Newcastle supporters who made the journey to Goodison to celebrate with a little more confidence that the three points would be heading back to Tyneside.
Wilson then grabbed his second just a few minutes later but any thoughts of a grandstand finish from Everton were unfounded as McNeil's effort proved to be mere consolation when substitute Isak set up Murphy for a goal line tap in after some of the most sublime skills saw Isak turn an ever chasing posse of Everton defenders not once, not twice but in some cases three and four times as he danced first down the touchline then the byline to give Murphy his third goal in two games.
This may prove to be a costly defeat for Everton in their fight to avoid the drop and they must now pick themselves up when they head to the King Power on Monday to face fellow strugglers Leicester City - the start of five vital games in a bid to avoid relegation from the top-flight for the first time in 72 years.
Newcastle United meanwhile return to action on Sunday afternoon when the visitors to fortress St James’ Park are bottom club Southampton. And while three points won’t see the champagne corks popping just yet, the toon army will certainly be in the spirit to get the party started!