Hatem Ben Arfa marked his full debut for Newcastle with the winner in a 1-0 victory at Goodison Park.
The Magpies deservedly picked up their first away win of the season and ensured Everton's miserable start continued after Ben Arfa's magnificent strike flew into the top corner of the net.
However, the hosts should have picked up an equaliser when Aiyegbeni Yakubu hit the post in injury time.
The Toffees were dealt a blow before kick-off when Tim Cahill failed a fitness test on his knee injury and when play started, the first notable incident saw Jermaine Beckford booked for a late challenge on Steve Harper, who landed heavily on his shoulder. He played no further part in the game.
Newcastle's substitute goalkeeper Tim Krul made his first save a few moments later from Leon Osman, although, after a decent run, the midfielder failed to make the best contact.
Ben Arfa then made himself an instant Newcastle fans' favourite with a superb 25-yard shot that flew into the top corner on the stroke of half-time. It nearly got worse for the Toffees in the 54th minute, when a deep cross from Jose Enrique was sliced wide of his own goal by Sylvain Distin.
At the other end, the home side created one of their best moments of the match when Osman's blocked shot found its way to Yakubu, whose scrambled effort was blocked by Krul.
The Nigerian felt he was impeded but referee Andre Marriner was unmoved and a spell of Everton pressure ended when Marouane Fellaini was shown a yellow card for throwing an arm at Mike Williamson.
Newcastle came close to grabbing a second goal in the 72nd minute when Ben Arfa jinked his way through again before playing in Andy Carroll, who was denied by a good challenge from Leighton Baines.
The visitors looked unfortunate not to be awarded a penalty when Seamus Coleman appeared to bring down Kevin Nolan in the closing stages. Then a well-worked free-kick on the left saw Baines find Yakubu - only for his shot to bounce off the post and onto Krul's back.