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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5. Jamaal Lascelles - 7
Dealt with things well in the air. Unfortunate with the own goal but helped Newcastle respond quickly and kept things relatively tight at the back. Photo: Stu Forster
6. Matt Targett - 7
Was well positioned and timed his tackles well to thwart a number of Everton attacks. A solid, no nonsense debut. Photo: Stu Forster
7. Jonjo Shelvey - 7
Had a couple of teasing shots early on. Another solid display. Booked. Photo: OLI SCARFF
8. Joe Willock - 8
After a slow start, really grew into the game and made the difference in the second half. Played a crucial role in the build-up to Newcastle's second goal. More like the player we saw last season. Photo: Stu Forster