Karl Darlow's error in the 27th minute gifted the Toffees their opener - which proved as the eventual winner from Wayne Rooney.
To add to Newcastle's misery, Jonjo Shelvey got himself sent off in the final minutes following a second yellow card.
The Newcastle supporters headed into the game full of optimism due to the reports that Amanda Staveley had tabled a £300 million offer to Mike Ashley to buy the St James’ Park club. But despite seeing the better side of possession, that failed to impact the result for Rafael Benitez’ with only one-point separating them from the relegation place.
For the Toffees, they won on the road for the first time in 17 away matches.
Four changes to Magpies starting line-up
Benitez made four changes to his starting 11 after losing to Leicester City 3-2 on Saturday. Captain Jamaal Lascelles returned in place of Ciaran Clark. Isaac Hayden dropped down to the bench as Jonjo Shelvey replaced him. Matt Ritchie retained his involvement ahead of Jacob Murphy, with Christian Atsu being preferred. The surprise inclusion of Mohammed Diame saw him start instead of Joselu, meaning Dwight Gayle started up top by himself - resulting in a 4-5-1 formation.
Bright beginning but errors cost Magpies again...
The Magpies' players took slight inspiration from the pre-match momentum to emerge as the stronger side in the first half, though found themselves behind through another mistake.
DeAndre Yedlin and Atsu looked threatening on the right-hand side but it was the other wing that brought the hosts their biggest joys.
Despite looking lively, it had taken until the 19th minute for Newcastle to register their first effort on target as Ritchie’s low drive was well held by Jordan Pickford.
And although the home side seemed in control, the game quickly swung in Everton’s favour within the space of a minute.
Just as the Geordie-faithful were off their seats ready to celebrate Ritchie’s shot that cannoned off the bar, the visitors broke, and undeservedly went in front.
Dominic Calvert-Lewin carved out a cross on the right wing, the small height of Aaron Lennon embarrassingly won the header before Darlow spilled it with Rooney alert to slide it in.
Benitez has spoken in recent weeks about individual errors costing his side, and Darlow’s was no different. Unfortunately for the former Nottingham Forest man, there was no hiding from that one.
Woodwork denies Newcastle for the second time
As well as United being the founder of their own downfall, the woodwork was also appearing as their worst enemy.
Mikel Merino, with time on the edge of the area, unleashed a stunning shot with only the inside of the post keeping the Magpies at bay with Pickford beaten.
Atsu maintained his bright return to the starting line-up when he wriggled his way into the box in the 44th minute before laying it off to Gayle, but he could only hit straight at Pickford.
The home side headed into the break with a lot of positives to take but were left rueing Darlow’s error.
All the possession, but no cutting edge for the hosts
Newcastle were certainly not one for lacking confidence at the beginning of the second period by continuing in the same positive fashion.
A leveller crept only millimetres away from the feet of Diame when Florian Lejeune headed Shelvey's free-kick towards goal – agonisingly missing the inside of the far post with the Senegalese man lurking.
With the Magpies seeing plenty of the possession but lacking that final spark, Benitez switched to a 4-4-2 formation – introducing Joselu for Diame.
However, it nearly resulted in near-disaster for the home side as Manquillo was intercepted Idrissa Gueye. The midfielder opted to find Gylfi Sigurdsson in miles of space, and with time to pick his spot, fired way high of Darlow’s goal.
The Toffee’s first sniff in the second 45 seemingly inspired them to search for a second goal as Ashley Williams saw his header brilliantly clawed behind by Darlow.
Everton’s upturn in possession forced Benitez into his second substitution with the pace of Rolando Aarons replacing the tired legs of Ritchie.
But for all of Newcastle’s possession, the lack of options in attacking areas allowed Everton to see out a comfortable victory and extend their unbeaten run to five in the Premier League.
To add to United's woe, Shelvey received a second yellow card in the dying stages.
The Newcastle supporters go home praying Staveley's takeover is imminent as relegation trouble continues to be heard around Tyneside.