The Magpies raced into a two-goal lead against the Hammers, only to be pegged back before loanee Joe Willock scored a towering header late on the seal all three points.
The results moves the Toon Army eight points clear of the bottom three with six games to go, and their cause was helped further when Fulham could only muster a draw against Arsenal on Sunday.
Speaking after Saturday’s clash, former Newcastle boss Graeme Souness admitted that he believed their win against West Ham will be enough to ensure their Premier League survival this season.
He said: “Enormous, and I think that will be enough for them.
"For West Brom, who have a bit of momentum, they’ll look on this result as a real kick in the teeth, and on Fulham also. I think they’ll be okay now.
"They did it in a fashion which won’t make Steve Bruce too happy. They were in the driving seat and they completely lost the plot with the other team down to 10 men, but they got there.
"They got a couple of large slices of luck. They will look back on the season and think that in the other games the luck has not been with them. Today they’ve got it and they’ll take it.
"I think that will be enough for them.”
Here are today's biggest transfer stories and the latest team news involving Newcastle and the rest of the Premier League, as the reaction to last weekend's action continues:

. NEWCASTLE UPON TYNE, ENGLAND - APRIL 17: A general view of St James' Park during the Premier League match between Newcastle United and West Ham United at St. James Park on April 17, 2021 in Newcastle upon Tyne, England. Sporting stadiums around the UK remain under strict restrictions due to the Coronavirus Pandemic as Government social distancing laws prohibit fans inside venues resulting in games being played behind closed doors. (Photo by Stu Forster/Getty Images)
St James' Park. (Photo by Stu Forster/Getty Images) Photo: Stu Forster

. Robinson talks up Heaton move
Paul Robinson has heaped praise on ‘phenomenal’ Aston Villa goalkeeper Tom Heaton, and has suggested that he would be a good signing for Leeds United or Burnley this summer. (Football Insider) (Photo by Nathan Stirk/Getty Images) Photo: Nathan Stirk

1. Robinson talks up Heaton move
Paul Robinson has heaped praise on ‘phenomenal’ Aston Villa goalkeeper Tom Heaton, and has suggested that he would be a good signing for Leeds United or Burnley this summer. (Football Insider) (Photo by Nathan Stirk/Getty Images) Photo: Nathan Stirk

2. Hornets in for Darlow?
Newcastle United goalkeeper Karl Darlow could be offered the chance to join Watford this summer. (Mirror) (Photo by STU FORSTER/POOL/AFP via Getty Images) Photo: STU FORSTER

3. Leeds rekindle Kent interest
Leeds United want to sign Rangers winger Ryan Kent in a £15 million move. (The Scottish Sun) (Photo by Ian MacNicol/Getty Images) Photo: Ian MacNicol

4. Spurs warned off Dunk
Tottenham legend Graham Roberts has warned Jose Mourinho about signing Lewis Dunk this summer, suggesting the Brighton centre-back is not going to get his old side back into the Champions League. (Football Fancast) (Photo by Clive Brunskill/Getty Images) Photo: Clive Brunskill