David Moyes' team were looking to build on last week's incredible comeback against Manchester United at Goodison Park on Saturday but the visitors fully deserved their three Premier League points, secured when winger Ben Arfa drilled an unstoppable shot into the top corner just before half-time.
The only sour note of a great afternoon for the Magpies was an injury to goalkeeper Steve Harper, who fell heavily on his left shoulder and was carried off on a stretcher.
For the hosts, who have mustered only two points from their opening five games, there were few positives to take, although they almost repeated last week's heroics when Aiyegbeni Yakubu hit the post in injury time.
Everton were dealt a blow before kick-off when Tim Cahill failed a fitness test on his knee injury while Phil Neville was only fit enough for a place on the bench, meaning Mikel Arteta kept the captain's armband.
The early stages were largely cagey, although both teams created one decent chance. Firstly Ben Arfa sent Jose Enrique sprinting down the left before delivering a cross that Wayne Routledge could only head over the bar.
In the 16th minute Everton went even closer, with Tony Hibbert curling over a superb cross that Phil Jagielka should have buried instead of powering his header wide.
The Magpies were certainly the dominant side and Joey Barton forced Howard into a decent save with a free-kick from 25 yards out on the half-hour mark.
Moments later the American was called into action again as Kevin Nolan's cross deflected off John Heitinga and was dropping under the bar until Howard stuck out a hand.
Jermaine Beckford then became the first player into referee Andre Marriner's book for a late challenge on Harper, which ended the Newcastle goalkeeper's involvement in the game.
Although the tackle was not a particularly bad one, Harper came down heavily on his left shoulder and immediately looked in distress.
Tim Krul was therefore thrust into the action, and he made his first save moments later from Leon Osman, although, after a decent run, the midfielder failed to make the best conduct.
Having shown flashes of brilliance, 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.
Moyes would have expected much better from his side and he reacted by bringing on Seamus Coleman and Yakubu for Hibbert and Beckford at the start of the second half.
It nearly got worse for the Toffees in the 54th minute, though, when a deep cross from Enrique was sliced wide of his own goal by Sylvain Distin.
At the other end the Toffees 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 Marriner was unmoved and a spell of Everton pressure ended when Fellaini picked up a booking for a foul on the impressive Mike Williamson.
Indeed, the Belgium international looked slightly fortunate to stay on the pitch after throwing an arm at Williamson.
There was no doubt the home side were now in the ascendancy, though, and Newcastle did well to hold firm when Arteta rolled a ball along the six-yard line.
Newcastle were largely reduced to hitting Everton on the break and they came close to grabbing a second 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.
Ben Arfa then went down theatrically under a challenge from Distin, but moments later the visitors looked very unfortunate not to be awarded a penalty when Coleman appeared to bring down Nolan from behind with the Magpies captain bearing down on Howard.
Ben Arfa was replaced by Jonas with six minutes left, receiving a rapturous reception from the Newcastle fans, but their hearts would have been in their mouths as the match entered added time.
A well-worked free-kick on the left saw Baines find Yakubu and his shot bounced off the post and onto Krul's back, with the keeper able to grab the ball before it crossed the line.
Everton were not finished and looked certain to level when Baines appeared to have found Fellaini six yards out but Fabricio Coloccini just managed to deflect the ball behind.