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 Thierno Barry failed to connect with the ball when well placed, but there has been no breakthrough yet as the Magpies look to bounce back from defeat against the Toffees in the Carabao Cup last week.
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.
**Newcastle United:** Lukáš Horníček, Lewis Hall, Fabian Schär, Nico González, Joelinton, William Osula, Harvey Barnes, Anthony Elanga, Joe Willock, Dan Burn (c), Amar Dedić
**Substitutes:** Nick Pope, Sven Botman, Aladji Bamba, Yoane Wissa, Malick Thiaw, Sean Steur, Bazoumana Touré, Jacob Murphy, Jacob Ramsey