Two own goals in two minutes from Jamaal Lascelles and Mason Holgate at either end saw the sides go in level at the break.
Ryan Fraser gave The Magpies the lead after the restart with his first league goal for the club. Kieran Trippier then secured the three points with a stunning free-kick to make it 3-1 late on.
Eddie Howe made just one change from the side that beat Leeds United in their last Premier League outing as deadline day arrival Matt Targett replaced Paul Dummett at left-back.
New signings Dan Burn and Bruno Guimaraes were named on the bench for the crucial encounter against The Toffees.
Our writer Dominic Scurr hands out his player ratings from the big win at St James’s…
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9. Joelinton - 7
Saw a close range effort saved by Pickford and comically lost his footing after being set up in a good area. For all his good work in midfield, still lacking in front of goal. Photo: Ian MacNicol
10. Ryan Fraser - 8
Gave Newcastle the lead by being in the right place at the right time. Made things difficult for Everton throughout the evening. Photo: Stu Forster
11. ST: Chris Wood
Joined Newcastle from Burnley for £25million this month. Hasn't set the world alight in the two matches he's played but boasts a solid scoring record in the top flight. Photo: PAUL ELLIS
12. Allan Saint-Maximin - 9
Everton tried to make his evening as difficult as possible but he stood up to the challenge well and remained a real threat. Played a key role in the second goal and deserved one himself. Photo: Alex Livesey