They had lost on their last five Premier League trips to Everton without scoring but took the lead after 19 minutes when Salomon Rondon lashed past Jordan Pickford.
Everton responded to dominate the rest of the half and were shouting for a penalty after a challenge on Ademola Lookman.
Richarlison had an effort saved but from the resulting corner the Brazilian stabbed home at the far post.
Everton looked the more likely winners but it was Newcastle who went close twice late on with Christian Atsu guilty of wasting a glorious chance for the visitors, shooting straight at Pickford as the clock reached 90 minutes.
Newcastle are still looking for their first win at Everton since 2010. (Reporting by Martyn Herman Editing by Toby Davis)
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