The left boot of Norwegian defender John Arne Riise knocked the stuffing out of Hammers inside the first nine minutes, in which the visitors took a two-goal lead through goals by Milan Baros and Steven Gerrard.
Baros nearly made it 3-0 on 15 minutes but he shot a yard wide of the far post. Not that it would prove costly for the Merseysiders, who punished hapless Hammers for more poor defending with a third by Emile Heskey on 66 minutes.
Liverpool's grip on the game was so strong, they could afford to leave Michael Owen on the subs' bench and didn't call on him until the game was well won with 18 minutes left.
For West Ham, showing two changes from the side that beat Blackburn, there were precious few plusses to take from this, one being another promising performance from young right-back Glen Johnson who kept going, delivered several excellent crosses from advanced positions and who was blameless for the goals.
Maybe the Rovers game took too much out of Paolo Di Canio after such a lengthy absence but, for once, neither he nor Joe Cole, whom Hammers rely on for inspiration, were able to make an impact.
In fact, Di Canio and strike partner Les Ferdinand struggled to stay onside in a first-half littered with seven offsides against the front two, who were not given any time or space by Liverpool's well organised back four.
Alas, at the other end, Baros and Heskey, with El Hadji Diouf wide on the right, were a constant handful for Tomas Repka and Christian Dailly, who came in for flu victim Ian Pearce in the troubled central defensive area.
Riise caused panic with two trademark inswinging free-kicks, the second of which led to Reds' first goal after only seven minutes. Riise's corner found the unmarked Baros, who nodded home from six yards.
Two minutes later and another Riise corner on Liverpool's right, down by the south-west corner of the Boleyn, saw David James rush from his line to punch. But he didn't make a clean connection and his clearance was driven back through the pack by Gerrard and into the bottom left-hand corner of the net.
Stunned by the double blow so early in the game, Hammers didn't muster a shot in the direction of Jerzy Dudek's goal until Lee Bowyer, who is eager to take all set pieces, clipped a tame free-kick harmlessly over from a good position 18 yards out.
At least Bowyer showed a willingness to venture forward whenever possible and he missed a half-chance when failing in an acrobatic attempt to convert Johnson's fine cross three minutes before half-time.
But the start of the second half mirrored the opening to the first, with Sami Hyypia - unmarked in the box - heading another Riise corner narrowly wide.
It was clear that change was needed if Hammers were to even threaten a fightback, so no-one was surprised when Fredi Kanoute left the bench five minutes after the interval. But instead of being given the chance to forge a powerful twin spearhead with Ferdinand, the former Spurs striker was the man to make way for the Frenchman.
Kanoute announced his arrival by scooping a shot over the bar after Bowyer had seen his effort blocked, and the Frenchman went closer seconds later with a rising volley after a knockdown by Trevor Sinclair, who returned to the right flank in place of the suspended Steve Lomas.
Glenn Roeder delayed new signing Rufus Brevett's debut until the 58th minute, when the dreadlocked left-back replaced Nigel Winterburn. Roeder was about to complete his trio of substitutions in the 66th minute, but before Jermain Defoe could get on for the ineffective Sinclair, Liverpool had killed the game at 3-0.
For the third time, one of Liverpool's eight corners in the match caused disarray in the home defence. This time Hyppia was allowed to climb unchallenged at the far post and nod the ball back across the goal, where James was disappointingly beaten to the punch by Heskey.
It ripped the heart out of the men in claret and blue and the long-suffering fans who, on this occasion, seemed to accept this latest defeat with a weary air of resignation.
The last 20 minutes were played out in a muted atmosphere more in keeping with an end-of-season mid-table affair.
If James and his central defenders endured another afternoon to forget, there was no solace for the forwards either. Cole, whose frustration is growing more visible (he was booked for throwing the ball away at a free-kick) didn't spot Di Canio in acres of space on the left during one rare breakaway. And when his delayed pass to Kanoute on the opposite flank finally reached the Italian, Hammers' playmaker delayed his shot too long to enable Dudek to make the block.
Roeder didn't try to disguise his team's failings again. He said: 'I didn't feel that we competed well enough all afternoon. From our point of view, they were cheap goals. People have got responsibilities at set pieces and those duties weren't carried out today.
'Believe me, we do plenty of work on set pieces at the training ground but it comes down to individuals fulfilling their responsibilities.
'I also thought we were too fearful and didn't get close enough to their players. Some - not all - need to roll up their sleeves.'
Roeder agreed that young Glen Johnson emerged with credit, adding: 'Glen has stepped up in class in recent weeks and acquitted himself very well. We are well pleased with him.'
The Hammers boss also said that he is ready to start Kanoute in next Saturday's game at Leeds.
Minute-by-minute:
3 - An early scare for the Hammers, as Riise's dangerous free-kick from the right finds its way through to the far post, where Heskey is just inches away from making contact.
6 - GOAL. After another Riise free-kick isn't properly dealt with and only cleared for a corner, the Norwegian's subsequent kick reaches Baros, who rises above the static Repka to fire a simple header past James from six yards out. West Ham United 0 Liverpool 1.
9 - GOAL. Double disaster for the Hammers, as another Riise corner causes panic. James opts, correctly, to punch clear, but Di Canio fails to clear the loose ball on the edge of the area and Gerrard unleashes a blistering right-foot shot that flies into the bottom right hand corner of the net. West Ham United 0 Liverpool 2.
25 - Hammers at last begin to threaten a response, as neat build-up play involving Bowyer, Di Canio and Ferdinand ends with Carrick being fouled on the edge of the area, but Bowyer curls the free-kick high and wide.
27 - Gerrard's left-footed effort is only parried by James, but Smicer is forced out wide as he attempts to convert the rebound.
42 - Johnson's dangerous cross from the right reaches Bowyer, who fails to connect with an attempted overhead scissors-kick.
Added time: 1 minute.
Half-time: West Ham United 0 Liverpool 2.
Second Half:
50 - Hyypia rises, unmarked, to meet a Riise corner, but thankfully heads his effort wide.
55 - Substitution for West Ham, Kanoute replaces Ferdinand.
57 - The arrival of Kanoute appears to have lifted the Hammers, and the Frenchman goes close with his first touch, volleying over after Carrick's touch into the area.
59 - Kanoute goes even closer, again with a volley that flies just inches over the crossbar after Sinclair has nodded down Cole's crossfield pass.
67 - GOAL. A third and vital goal for Liverpool, as another Riise corner looks to be heading out of play at the far post but is nodded back by Hyypia into the six-yard box, where James is beaten to the ball by Heskey. West Ham United 0 Liverpool 3.
68 - Substitution for West Ham, Defoe replaces Sinclair.
73 - Substitution for Liverpool, Owen replaces Baros.
74 - An excellent chance for West Ham to try and salvage something goes begging, as Kanoute's low cross finds Di Canio at the far post and the italian cuts inside but sees his team's first shot on target of the match well saved by Dudek
79 - Substitution for Liverpool, Cheyrou replaces Smicer.
79 - Cole booked for dissent.
82 - Substitution for Liverpool, Hamann replaces Murphy.
83 - Johnson's superb cross from the right is headed over by Carrick
Added time: 2 minutes.
Full-time: West Ham United 0 Liverpool 3.