David Moyes' side found themselves 2-0 down inside 13 minutes against the Magpies, a shocking start for the home side in desperate need of points.
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Callum Wilson gave Newcastle the lead in the sixth minute with a simple header, but Joelinton's 2-0 goal was even easier.
Stunned by the defending, talkSPORT's in-ground reporter Ian Abrahams said: "God this is Sunday league stuff.
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"It's one straight pass through the middle for Joelinton to run onto, he's round [Lukasz] Fabianski and scored.
"After the usual three minute VAR check it's of course onside, it's a shocker of a goal to concede."
Kurt Zouma pulled one back for the Hammers on 40 minutes but the relegation-threatened side gave themselves a mountain to climb at the start of the second half as Wilson got his second and Newcastle's third of the night.
It was woeful from a West Ham perspective as Hammers defender Nayef Aguerd was dispossessed on the edge of his own box by Jacob Murphy.
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Murphy then squared the ball to Wilson, who tapped it into an empty net.
After the goal, Abrahams said: "This is schoolboy defending."
The terrible defending didn't stop there as Alexander Isak made it 4-1, lobbing Hammers goalkeeper Lukasz Fabianski after the Poland international made a complete hash of a clearance.
Joelinton then made it 5-1 as his left-footed effort went through the hands of Fabianski.
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The result means West Ham are only out of the bottom three on goal difference, while Newcastle's bid to finish in the Champions League spots continues to gather momentum as they remain third.