After a goalless first half, the Magpies got themselves ahead from the penalty spot when Callum Wilson converted from twelve yards before he tapped in a Ryan Fraser cross to give his side a two-goal lead going into the closing stages.
Dominic Calvert-Lewin did pull one back in the dying moments but given the amount of time remaining in the game, an Everton comeback was never likely.
But this also seemed the case back in January 2020 when the Magpies last visited Goodison Park, and on this occasion it was Florian Lejeune who grabbed his first Newcastle goal with an acrobatic overhead kick in the fourth minute of four added on.
What happened next seemed improbable...
So what did happen?
Everton found themselves a goal to the good at the break thanks to Moise Kean's first Premier League goal and with Newcastle putting in a poor showing on Merseyside, it looked like there would only be one winner.
When Calvert-Lewin added a second for Carlo Ancelotti's men ten minutes in the second half it was starting to look a case of how many Everton could get for themselves.
So into stoppage time we go and four minutes is signalled by the fourth official with the score still 2-0 to the hosts. A few of the Newcastle fans in the away end had disappeared and left the ground early to avoid the post-match crowds. Who can blame them when the performance was as poor as it was on that Wednesday night?
It's the fourth minute of added time at Goodison Park and referee Simon Hooper signals a corner for Steve Bruce's side. Could they at least grab a consolation?
Yes they could was the answer and after some questionable goalkeeping from Jordan Pickford, a man Newcastle fans can't stand, Lejeune was on hand to fire into the back of the net with a finish that any top striker would be proud of.
Straight from the re-start after Lejeune's acrobatic's, Everton were sloppy and gifted possession straight back to Newcastle who then won a free-kick, albeit nearer the half-way line than the opponent's goal.
The experienced Ancelotti on the sidelines was furious with his team's inability to effectively manage a game.
A couple of extra minutes had been added on after the scuffle that came with Toon players optimistically rushing to get the ball back for the re-start.
It was almost as if they knew what was going to happen next, but in typical Newcastle style they didn't do it the orthodox way.
The free-kick was played short, as you do when you're searching for a goal. But in the end Matt Ritchie did launch the ball forwards and caused havoc in the Everton box.
It looked as if the Toffees had escaped after multiple efforts from Newcastle players appeared to have been cleared. But wait, Simon Hooper looked at his watch and realised that the ball had actually crossed the line, sending the Magpies' players and remaining fans bonkers in the stands, meanwhile the same couldn't be said for those of an Everton persuasion who couldn't believe that their improving side had, quite frankly, bottled it.
After a post-match inquest, it was eventually concluded that Lejeune was the man who managed to get the ball over the line so just like London buses, his first two, and still only goals for Newcastle came in the space of just a few short minutes.
The next meeting
Newcastle will return to Goodison Park on Saturday as they kick-start the next round of Premier League fixtures against Everton at lunch time (12:30pm). The game is live on BT Sport.
The Magpies are massively out of form having failed to win any of their last eleven matches, the latest negative result being a 2-1 defeat to Leeds United in midweek.
Everton's midweek outing saw them held to a draw against high-flying Leicester City.