Success against Burnley in their last outing opened up a six-point gap between the Magpies and the current bottom three, with seven games left to play.
Another win this weekend could see their cushion plumped up to nine points, assuming Fulham lose against Arsenal.
Manager Steve Bruce will be grateful to have talisman Allan Saint-Maximin back in contention for a start too following his match-winning cameo against the Clarets.
Speaking after that game, Bruce said: “Allan’s missed half a season.
“They [Saint-Maximin and Callum Wilson] both had muscle injuries, so I think it made sense [to start them on the bench.
"They made an impact. Probably only Allan can do that. Let’s hope they stay well.
“That’s been the key. I think that was his [Saint-Maximin's] 18th appearance. Our big players haven’t been available. You need your big players. He’s a very talented player, who hasn’t been available for half a season. It’s been a struggle without them.”
“It’s three points towards that magical figure. You’ got to gt to that figure. It [the club’s position] is certainly a lot more healthy today than it was this morning.”
Newcastle actually beat the high-flying Hammers when they last met in the top flight, with Callum Wilson and Jeff Hendrick scoring the goals in a 2-0 win on the opening day of the season.
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:
5. Blades could hand Ndiaye new deal
Sheffield United could choose to reward youngster Iliman Ndiaye with a new contract following his recent progress, despite still being without a permanent manager following Chris Wilder’s departure last month. (The Star) (Photo by Laurence Griffiths/Getty Images) Photo: Laurence Griffiths
6. Brighton in for Styles
Brighton are readying a bid to bring Barnsley midfielder Callum Styles to the South Coast this summer, but will have to pay over £8million to make the move happen (The 72) (Photo by Clive Rose/Getty Images) Photo: Clive Rose
7. Jokanovic likely to move
Sheffield United target Slavisa Jokanovic is unlikely to stay at Al-Gharafa for another season, and wants to be reunited with his family in Europe. (The Star) (Photo by Alex Livesey/Getty Images) Photo: Alex Livesey
8. Leeds offered Moreno
Leeds United are in the hunt for 27-year-old left-back Alex Moreno. West Ham are also keen. (TeamTalk) (Photo by Fran Santiago/Getty Images) Photo: Fran Santiago