At a glance
Malick Thiaw heads Newcastle in front from Lewis Miley's corner after just 55 seconds
Miley doubles Newcastle's lead after error from Everton goalkeeper Jordan Pickford
Nick Woltemade adds third before half-time with cool lobbed finish
Thiaw scores another header in second half before Kiernan Dewsbury-Hall nets delightful consolation for Everton

Newcastle United had failed to win any of their previous nine away league games
Newcastle United head coach Eddie Howe enjoyed a 48th birthday to remember as his side ended their long wait for an away win in style against Everton.
The travel-sick visitors had failed to win on the road in the Premier League since April.
But aggressive Newcastle started as they meant to go on at the Hill Dickinson Stadium by scoring the quickest goal of the season so far in the top flight.
Defender Malick Thiaw jumped ahead of Michael Keane to power a header past Jordan Pickford and net his first goal for the club from Lewis Miley's in-swinging corner.
Though Everton rallied, initially, after going behind after just 55 seconds, the hosts only had themselves to blame for Newcastle's second goal.
Not only did Everton defenders fail to clear their lines following some pinball inside the box, Pickford failed to keep out Miley's effort despite it being hit straight at him.
David Moyes, unlike a beaming Howe, looked understandably furious on the touchline, but the Everton manager's evening got even worse before half-time when Nick Woltemade added a third.
Tino Livramento clipped the ball down the line and Anthony Elanga hooked it across to the unmarked German, who nonchalantly lobbed Pickford from inside the area to score his seventh goal of the season.
Newcastle grabbed a fourth before the hour mark when Lewis Hall's teasing cross was headed in by Thiaw at the back post.
There was still time for Kiernan Dewsbury-Hall to pull one back for Everton after the midfielder brilliantly controlled James Tarkowski's ball over the line before slotting past goalkeeper Aaron Ramsdale.
But it was always going to be a mere consolation as Newcastle leapfrogged Everton in the table and moved up to 11th place.
Newcastle analysis: Howe's big calls pay off
First away win is a big step forward for Newcastle form - Howe
This felt like a huge win for Newcastle - in so many ways.
Howe had grown tired of talking about his side's issues away from home but, finally - following a 236-day wait - they delivered on the road in the Premier League.
The Newcastle head coach rang the changes following the midweek defeat in Marseille - and those calls certainly paid off.
Ramsdale, Miley and Elanga were among those handed rare starts while regulars like Joelinton, Hall and Woltemade also came back in.
Ramsdale may have conceded late on, but the goalkeeper was assured on his first league start in place of the injured Nick Pope and calm in possession.
Miley set up his side's opener before making it 2-0 as he became the second-youngest Newcastle player ever to score and assist in a Premier League game.
And the rapid Elanga looked more like himself following a challenging start since his £55m move from Nottingham Forest.
Yet it was a change of mentality as much as personnel.
As Everton started to probe, after going behind so early on, Newcastle protected Ramsdale, with Dan Burn and Hall both making crucial blocks inside the box and even forward Woltemade getting back to cut out a cross from Jack Grealish.
Though Pickford ended up giving Newcastle a huge helping hand, crucially, Newcastle managed to double their advantage, which they failed to do when ahead on their travels against Marseille, Brentford and West Ham in recent weeks.
They did not look back from there as Everton crumbled.
No wonder the away end repeatedly sang about how they did not want to go home as the game drew to a close. This victory had been a long time coming.
Everton analysis: Back down to earth for Toffees
Newcastle are probably the most physical team in the league - Moyes
Ten-man Everton showed plenty of fight to win at Old Trafford on Monday.
Perhaps a little too much after midfielder Idrissa Gueye was sent off for slapping team-mate Michael Keane.
But Everton never truly recovered from going behind so early on in this game.
Just when Everton appeared to rally, and started to dominate possession and force Newcastle back, the hosts gift-wrapped a second even before Pickford's error after both Michael Keane and Tim Iroegbunam failed to clear.
Elanga then went on to shake off Iroegbunam far too easily in the build-up to Woltemade's third.
It was rather telling that Moyes hauled off Iroegbunam at half-time but, in truth, he could have substituted a host of his under-performing players.
But this was a rare off day at the Hill Dickinson.
Everton have enjoyed life at their sparkling new home since leaving Goodison Park, losing just two games.
But when Moyes' side have lost, they have ended up well-beaten - as was also the case in their only other defeat at the Hill Dickinson Stadium, a 3-0 reverse against Tottenham Hotspur last month.
Everton bounced back from that defeat by picking up seven points from their next three games.
They have to ensure they do so again.
What next for these teams?
Everton travel to Bournemouth on Tuesday, 2 December (19:30 GMT) before hosting Nottingham Forest at the Hill Dickinson Stadium on Saturday, 6 December (15:00 GMT).
Newcastle welcome Tottenham Hotspur to St James' Park on Tuesday, 2 December (20:15 GMT) before another home game against Burnley on Saturday, 6 December (15:00 GMT).
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