A deflected shot from Xavi Alonso and Bolo Zenden's late strike off a post separated them from West Ham, although they had the opportunities to put the issue beyond dispute long before the Dutchman's goal. Fernando Morientes squandered two, second half chances and West Ham's goalkeeper, Shaka Hislop saved athletically from Louis Garcia to prolong the semblance of a contest.
But therein lies what should be the lingering concern from Liverpool and their manager, Rafael Benitez. Goals remain elusive for their strikers. Morientes is a shadow of the once majestic player, a yard too slow in the frenzy of the English game and lacking the conviction to capitalise on his aerial prowess. His partner in this match, Djibril Cisse, had one of those exasperatingly ineffectual days. The Frenchman does, at least, have the pace essential to outstrip Premiership defences but he ultimately made way for Zenden's arrival.
Steven Gerrard's restoration to the starting line-up inevitably raised expectations, although his impact was compromised by being stationed wide on the right. As a consequence, he was able to make fewer of those familiar, surging runs through the middle that inspired colleagues and terrorised opponents in equal measure.
Even so, his very presence palpably unsettled West Ham and eventually Liverpool's superiority subdued Alan Pardew's side. West Ham started with admirably positive intent and Nigel Rao-Coker again demonstrated his obvious talent. Yossi Benayoun fleetingly gave glimpses of his skills, too, but by the second half, he had become an almost anonymous figure, leaving Marlon Harewood, West Ham's sole out and out striker, an ever-more forlorn and remote figure. Just like their faded bubbles, West Ham faded and died as a force.
Benitez, not unreasonably, argued he would settle for this result every week, regardless of the scorers, but behind that stoic countenance he will surely be frantically trying to work out how he can find a consistent source of goals.
He said: "The strikers worked hard and if we win 2-0 every game it's okay. Even if (Jose, the Liverpool goalkeeper) Reina scores. All Morientes needs is to score.
It was an idea to use Steve wide and he did a good job. He can still come inside and he had the freedom to do that. It's possible we will play him there again."
Gerrard did have the freedom to step in to a more accustomed role when Zenden came on and the Dutchman made the most of Pardew's decision to take off his right back, Tomas Repka.
Pardew conceded: "You could blame me for the second goal. But we tried to do something. We were up against the European champions and we had some brilliant individual performance.
"But we didn't do enough to warrant getting back in the game after their first goal. We're a little disappointed we didn't show more relief to go and hurt them. They were focussed and Steve and Gerrard made a massive difference."
West Ham failed to muster a serious threat to Reina's goal and survived a few scares before Liverpool went ahead in the 18th minute. Alonso took careful aim from 25-yards but his shot still took a deflection off Repka on its way past Hislop.
Sami Hyypia had a shot cleared off the West Ham line by Paul Konchesky as Liverpool at last began to flick through the gears.
Morientes could have claimed that second goal but wanted more time than Anton Ferdinand prepared to permit him.
The Spaniard met Steve Finnan's centre with a characteristic header, only for Hislop, lunging down to his right, to save.
The goalkeeper made an even better save to deny Garcier but couldn't respond to Zenden's drilled effort in the 82nd minute.