Only goal difference separates Albion from a place in the bottom three and a run of one point from their past seven matches suggests that advantage will soon count for little.
Even without their talisman Steven Gerrard, suspended following his dismissal against Everton last weekend, Liverpool had far too much quality for Albion whose defensive frailties were cruelly exposed by Djibril Cisse.
The Frenchman scored once and created another for Robbie Fowler to bring Liverpool a fourth successive Premiership victory. He has a strange way of showing that he does not like playing on the right flank.
Indeed it was from that position that he created Liverpool's first goal inside seven minutes. Albion may well feel aggrieved that Fowler was not given offside, although Paul Robinson should also shoulder his share of the responsibility. The Albion left-back was caught the wrong side of Cisse, who accelerated forward before crossing to the back post where Fowler, advanced of the Albion defence, tapped in.
More torment was to follow for Robinson later in the half as Cisse continued to cause problems. There appeared little danger when Xabi Alonso seized possession on the edge of his own area, but a 60-yard pass from the Spaniard picked out Cisse's run across Robinson. Cisse still had much to do, but he adroitly evaded the challenge of Curtis Davies before rounding Tomasz Kuszczak and prodding home.
Albion's response was muted. Their confidence had been sapped by the alacrity of Liverpool's counter-attacking that might have yielded a third goal only for Peter Crouch to bundle his effort wide from Cisse's cross.
It took the introduction of Zoltan Gera at the interval to bring some much-needed penetration to the home side and the Hungarian came close to making an immediate impact when he curled a right-foot shot narrowly wide in the 46th minute. Five minutes later he troubled Jose Reina again, thundering a left-foot volley into the arms of the Liverpool goalkeeper, who saved from the same player later in the second half as Albion began to attack with renewed belief.
In between those two efforts Cisse came close to grabbing his second when he left the hapless Robinson trailing, but Kuszczak rushed from his line to save. The Albion keeper ought to have been beaten again late on but Fernando Morientes inexplicably missed from two yards.
'In the first half we played very well, deserved to score and controlled the game all the time,' said Rafael Benitez, the Liverpool manager. 'In the second half we were a bit under pressure and we could not score the third goal and finish the game. We need to keep going to the end - Manchester United continue winning but our idea is to do that also and maybe we can finish second.'
MAN OF THE MATCH: DJIBRIL CISSE Gave Albion a torrid time as he wreaked havoc down the Liverpool right. He showed awareness to set up the first goal for Robbie Fowler with a superb cross and then crowned it with a strike of his own.
