Thierno Barry tapped home after Tyrique George's shot squirmed beneath Lukáš Horníček early in the second half for a goal befitting of a game often lacking in quality.
Harvey Barnes started strongly, whipping in a couple of dangerous deliveries - one which drifted inches wide of Jordan Pickford's far post.
Then a William Osula cross deflected off James Tarkowski and almost caught Pickford out, but the visiting goalkeeper adjusted his body quickly to save.
In the 16th minute, Joelinton fired in a shot on the turn but Tarkowski blocked bravely. From the resulting corner, swung in from the right by Lewis Hall, Dan Burn headed off target.
A Merlin Röhl effort flew over the bar for Everton, then Barry failed to connect with the ball when well placed.
Pickford had to push over another bending Barnes ball after it looped up off Jarrad Branthwaite, then Joelinton sent a piledriver from 20 yards narrowly wide.
On the stroke of half time, Harrison Armstrong squandered a wonderful opportunity for the Toffees as he miscued from close range.
But Barry could not miss when George's shot wasn't dealt with by Horníček, allowing the Toffees' French frontman to give his side the lead.
Horníček had to push away a looping Branthwaite header soon afterwards as the Merseysiders pushed for a second.
Fabian Schär wasn't too far away from an equaliser with a half-volley from range but Kiernan Dewsbury-Hall brought a good save from Horníček at the other end.
Then the Newcastle netminder was called into action again with a fine stop low down from Branthwaite's downward header.
United thought they had levelled when Barnes dangerous delivery from the left hit Vitali Mykolenko but Anthony Elanga just couldn't force the ball home.
Substitute Jacob Ramsey drilled agoinsigly wide in the 79th minute, then Osula flicked a header the wrong side of goal.
A Yoane Wissa drive was easily fielded by Pickford - then the England goalkeeper used his feet to keep out a shot on the turn from the same player and earn his side the win.
And a miserable night was compounded when Ramsey was sent off after picking up two bookings in stoppage time.
Newcastle United: Lukáš Horníček, Lewis Hall, Fabian Schär, Nico González (Sean Steur 64), Joelinton (Jacob Ramsey 76), William Osula, Harvey Barnes, Anthony Elanga (Jacob Murphy 76), Joe Willock (Yoane Wissa 64), Dan Burn (c), Amar Dedić (Bazoumana Touré 87)
Subs not used: Nick Pope, Sven Botman, Aladji Bamba, Malick Thiaw




