Their position is made more worrying because the Latics have a game in hand and a better goal difference, but the clean sheet was a vast improvement on last weekend's 6-0 loss to Liverpool.
It was clear that the visitors arrived at Upton Park aiming to be more solid after that shattering defeat and the return of Fabricio Coloccini in the heart of their defence after injury was a welcome boost.
Now they must turn their attentions to their next match against relegated QPR, but the fact that their hopes are not entirely in their control underline the side's worrying loss of form.
Newcastle are also one point clear of arch rivals Sunderland, who also have a game extra, and in some senses this was an opportunity missed as West Ham, promoted from the Championship last season, are relatively comfortable in mid-table and remain 10th in the Premier League.
The Magpies have lost four and drawn one of their five Premier League away trips to London this season.
Newcastle failed to score for the fourth time in their last six Premier League matches. They netted only two overall in the other two games.
West Ham did not impose themselves on the game until after the break and as has often been the case this season, Matt Jarvis was the source.
His inviting cross after 48 minutes was headed wide by Carroll at the back post. Ricardo Vaz Te then failed to connect with another centre minutes later after being pushed by Coloccini.
That instigated a better spell for Allardyce's side, who almost went in front again, but Elliot's superb double save denied Nolan, while Carroll had another penalty appeal turned away by referee Phil Dowd.
Ben Arfa was replaced by Shola Ameobi and the substitute centre-forward fired wide after Yoan Gouffran went close with another effort, but as West Ham grew in confidence, the draw was well-earned and it might yet be an important point for Newcastle.
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