A 51st-minute strike from Theo Walcott separated the two sides, who both struggled in front of goal at Goodison Park.
Everton only managed one shot on target throughout the 90 minutes while Newcastle found the target twice but didn't really test Jordan Pickford.
It wasn't the highest-quality game in truth and it saw Everton manager Sam Allardyce once again slammed for the style of play he's introduced on Merseyside.
"What was wrong with our style today? We completely dominated the game, out-passed the opposition in their half," he added.
"We were patient and got the winner. Some of our passing went astray but in fairness you can't really blame me for that can you? I don't pass the ball out there, the lads do."
Newcastle manager Rafa Benitez, meanwhile, blamed the defeat on his players not taking their chances and the money Everton are able to spend on players.
EVERTON SCRAPE VICTORY
"We didn't take our chances and that is the difference when you have Walcott or [Wayne] Rooney or players on these wages that can make a difference," said the Spaniard.
"We did really well to be here to play against this team. To expect that we have to beat them easily is impossible. They have very good players and they can make the difference."
In fairness to Newcastle, they were on the receiving end of some pretty controversial decisions from referee Bobby Madley during the game.
It was in the 87th minute that Madley really frustrated Newcastle's players and fans when he waved away appeals for a handball on Phil Jagielka inside the box.
Replays showed Jagielka's arm was down by his side but he did poke it out slightly, so the visitors certainly had a case.
It turns out Madley didn't even see the incident, though, judging by his hilarious altercation with Newcastle's players afterwards.
In the video below, Madley can be seen repeatedly saying, "I didn't see it, sorry," before completely losing his rag and shouting, "I said I'm sorry!"
MADLEY'S HILARIOUS OUTBURST
Amazing. Newcastle's players were understandably furious and they wound up Madley so much that he shouted something you would expect to hear on a playground.
Embarrassingly it was one of the game's most exciting moments.