Richard Garcia was partnered with Neil Mellor up front as Don Hutchison started on the bench.
The game was only four minutes old when Mellor's raking drive from the right headed towards Garcia, but it took a touch off Norwich's Marc Edworthy to elude Green in goal and give the Hammers an early tonic.
Shortly after David James was brought into the action when Darren Huckerby saw off Dailly, his resulting effort forcing a good stop from the England number one shirt custodian.
His opposite number was called upon not long after when he made a brilliant save at the feet of Matthew Etherington, who nevertheless must have been disappointed to spurn a gilt-edged chance from only a few yards out.
Norwich's six foot seven-inch striker Peter Crouch proved to be the Hammers main tormentor, and after some great skill to ghost past Pearce his shot was poor and did not trouble James.
Etherington was similarly having a great game for West Ham, and after his pace took him past three defenders, again his shot was a disappoitment and flew wide.
Norwich started the second half brightly and nearly made David James pay for a poor clearance that went straight to Holt. He fed McVeigh and James made amends well to deny his shot.
Neil Mellor was lively again not long after and his excellent shot from 25 yards out brought a superb save from young Green in the Norwich goal.
Disaster struck for the home team after 17 minutes, when Wayne Quinn gave the ball away. The resulting move ended with Peter Crouch rising to head past James from six yards out. Things could have been worse two minutes later when Francis was only denied by the post after Harper & Crouch had sliced through the Hammers defence.
West Ham eventually gained the upper hand but could not turn their pressure into goals, the closest they came being when a Dailly header was saved under the bar by Green.
The game petered out as Norwich put ten men behind the ball and seemed content to hold out for a point. West Ham could not create anything in front of goal and they game ended quietly with very little goalmouth action towards the end.