Marlon Harewood began the scoring as early as the sixth minute when he rose highest to head home a corner from Michael Carrick.
With both sides looking to attack, the first half was proving to be an open affair and Crewe had several early chances to level the scores.
However, Harewood doubled the hosts' advantage midway through the half when he out out-muscled Steve Foster to run through and smash the ball past Clayton Ince in the Alex goal.
The second goal clearly boosted the confidence of the home side and they went in search of more goals before the break.
The third duly came when Harewood unselfishly laid the ball off to Nigel Reo-Coker who lashed in a brilliant right foot shot from the edge of the penalty area.
A rampant West Ham then made it 4-0 just before the break as Jobi McAnuff grabbed his first for the club as his left footed shot found the net via a post.
The second half continued to see chances at both ends and while Alan Pardew's side frittered away numerous possibilities to add to their lead, Crewe took advantage to cut the deficit with two quick strikes.
Steve Jones helped himself to a double as The Hammers defensive line proved fickle and left keeper Stephen Bywater exposed.
But the away side were unable to continue their fight back and received a further blow when their custodian Ince had to be stretchered off in the final ten minutes.
