The Hammers were ruthless with their hosts' poor defending inside a nine-minute first-half spell, going 3-0 up to effectively seal the three points with 65 minutes still left to play.
The Londoners' strike force of David Connolly and Jermain Defoe were too energetic and clinical for the Railwaymen, particularly in the first 45 minutes when Dario Gradi's side pressed the self-destruct button.
Connolly helped himself to two soft goals and Matthew Etherington fired in a screaming volley after Crewe had opened up brightly, buoyed by their weekend win at Rotherham.
Beating the likes of the Millers will be the key to the Cheshire side's chances of survival in the first rivision; as against the calibre of the Hammers they can only work hard to plug the gaps in class.
But they were let down by their defending when it mattered and West Ham took advantage and ran them ragged the rest of the half.
There was no danger when Steve Foster directed a back pass towards Clayton Ince in the 16th minute, but the delivery was under hit and Connolly kept his cool to jockey the ball into position to rifle high into the net
Ince was at fault when Wayne Quinn let fly with a 30-yard free kick, which dropped out of his hands and Connolly snaffled the chance for his second.
Crewe were reeling and their plight worsened when Christian Dailly headed down a corner and the ball sat up for Etherington to volley past Ince from outside the box.
Defoe came close to getting his side's fourth when he was put free on the right of the box, but Richard Walker deflected the shot wide for a corner.
Dailly had also seen an earlier header cleared off the line by Ben Rix before Crewe should have taken the lead .
If Steve Jones had been more clinical when the ball deflected into his path they would have done, but David James' reflexes kept the scores goalless with a reflex stop with his legs.
The three-goal blitz knocked the stuffing out of Crewe, but they did rally after the break and Dean Ashton came close on several occasions to reducing the arrears.
The teenager turned and fired just over after Justin Cochrane had slipped in a useful delivery and then he rampaged through forcing James to push his effort around the post.
Crewe: Ince, Wright, Walker, Foster, Tonkin, Lunt, Brammer, Cochrane, Rix, Jones, Ashton. Subs: Bankole, Sorvel, Varney, McCready, Edwards.
West Ham: James, Repka, Pearce, Dailly, Quinn, Lee, Horlock, Alexandersson, Etherington, Connolly, Defoe. Subs: Ferdinand, Kilgallon, Noble, Bywater, Mellor.
Yellow Cards:
D.Connolly, 88, unsporting behaviour
Referee: A Butler (Nottinghamshire)
Attendance: 9,575