Chances were few and far between as Newcastle secured what could yet prove crucial reward - but wins for Wigan and Aston Villa keep them looking over their shoulder.
The closest either side came to scoring was when Papiss Cisse saw his first-half effort cleared off the line by Winston Reid.
Newcastle welcomed back captain Fabricio Coloccini to the side after being out of action since February with a back problem and his presence helped organise their defensive line after conceding six last time out against Liverpool.
Hatem Ben Arfa, who was recalled to the starting line-up, tried his luck with a free-kick wide on the right on ten minutes with his dipping effort landing on the top of Jussi Jaaskelainen's net.
Newcastle went so close to breaking the deadlock on 20 minutes when Yohan Cabaye played Cisse in on goal and his scuffed shot was cleared off the line by Reid with Newcastle players appealing that the ball had crossed the line before the West Ham defender's intervention.
Ben Arfa was looking the man most likely to score and he had a chance on 25 minutes when he ran from halfway line into West Ham's penalty area only for his final shot to lack the power to trouble Jaaskelainen.
Andy Carroll was starved of service against his former club as West Ham failed to offer any real threat in the final third.
The game livened up a bit in the second half and Carroll had a chance four minutes after the break when he got on the end of Matt Jarvis' cross at the far post, but he could only head his effort wide of the target.
Carroll had another sight of goal on 57 minutes when Mohamed Diame picked him out inside the box, but under pressure the striker sent his header over the crossbar.
The home side had claims for a penalty waved away on 65 minutes when Carroll went down in the box after a tangle with Danny Simpson before the ball dropped to Jarvis who picked out Kevin Nolan at the far post only to see his close-range effort kept out by Rob Elliot and then his follow-up also blocked by the Newcastle keeper.
Newcastle went close to scoring three minutes later when Yoan Gouffran beat Jaaskelainen to a long ball over the top to go round the keeper, but his touch took him too wide and he could only loft his shot wide of the gaping goal.