Liverpool's first-half barrage secured an easy win over a West Ham side that looked worryingly weak at Anfield.
Former Hammer Glen Johnson cracked a low shot past over-worked Robert Green to give the hosts an 18th-minute lead.
Dirk Kuyt then coolly slotted home a penalty after lively Fernando Torres had caused Danny Gabbidon to handle.
Maxi Rodriquez nodded in a simple third before half time, while bottom-of-the-table West Ham created nothing in a largely stale second period.
Now with just one win in 14 Premier League matches this season, Avram Grant's Hammers were desperate for something positive from their trip to the north-west - a performance if not a tangible result - to convince supporters that their team is not destined for relegation.
But, at a ground where the club has not won since 1963, the Irons put in a poor show - one which could increase pressure on Grant just days after his board backed him to steer them clear of trouble.
The visitors - who have not won a league match on the road since the opening day of last season - were almost completely compliant, offering little resistance to a club equally in need of some cheer.
Impressive French youngster David Ngog forced a good early stop from Green after jinking his way into space before Raul Meireles, who appears to be winning over the Kop faithful, just failed to release Torres.
In the 10th minute, the Spaniard got his first chance after Ngog had danced across a line of dallying defenders.
But the World Cup winner smashed a low shot just wide of the post as the hosts set about dominating possession with almost embarrassing ease.
Radoslav Kovac did make a superb block with Torres ready to pounce again, before Meireles's stinging shot was tipped over by Green.
But the barriers inevitably burst, and it was England right-back Johnson who made the breakthrough.
Competing for the ball under more pressure from his team-mates than the opposition, he managed to chest a Meireles corner into space before zipping a low drive firmly past Green with consummate technique.
Johnson then did his defensive duties with a clearing header from a Kovac cross with Obinna lurking, but Liverpool continued to flood forward.
Torres - full of inventive running but still not yet hitting peak form - escaped easily down the wings time after time, but failed to find well-positioned team-mates in the box.
And - when Johnson chipped a cross to the back post - the former Atletico Madrid forward could only scuff a volley into the ground.
But Torres won the 27th-minute penalty, chipping the ball over Matthew Upson's foot onto Gabbidon's hand to leave the linesman flagging furiously for a spot kick.
Dutchman Kuyt finished down the middle as Green dived too early.
Full of frustration, West Ham's travelling support even began chanting the name of former player Paulo Di Canio as Lars Jacobson frantically cleared off the line following a desperate scramble in the box.
A decent chance did fall to Carlton Cole soon after, though the occasional England striker could not convert Luis Boa Morte's cross despite climbing high above the hosts captain Jamie Carragher to make a clean connection.
Yet that was a rare opening for a side seeming to lack any inspiration, and Liverpool added a crushing third soon after.
From a narrow angle, rampant Torres forced a smart save from the feet of Green but former Hammer Paul Konchesky steered a cross straight back into the box and Maxi angled a simple header across the visiting goalkeeper.
Grant did make a change at the break, bringing Victor Obinna off for Pablo Barrera, and changed his formation from 4-5-1 to 4-4-2.
But tactics seemed to have little relevance for the ambition-free Hammers as they failed to make any impression on the second 45 minutes, bar keeping a clean sheet and keeping the score respectable.
That tiny chink of consolation was threatened in the 67th minute, when Maxi burst forward into the box and almost lifted an inadvertent chip into the top corner of Green's goal from the left.
But the ball drifted just past the post before going out.
Green then made a stunning double stop when, firstly, he pushed Torres' powerful 20-yard shot onto the bar before tipping Christian Poulsen's equally
The rest of the action resembled a testimonial match as Liverpool closed out a win which will put each club in contrasting moods.