The Hammers conjured a chance when Cole headed wide from a Matthew Etherington corner before Tabb showed him how to do it, nodding in Osbourne's delightful forward ball on 68 minutes.
But West Ham's leveller stunned them and they soon found themselves behind when they failed to defend a corner, Matthew Upson heading back across goal for Neill to finish smartly.
The second chance came just before the interval - from West Ham's first corner - when Matthew Upson headed the ball on and Tristan flicked the ball goalwards only for Jon Mikel Obi to clear off the line.