Ian Rush's predatory instincts sealed the points for Liverpool with a goal three minutes from time.
The ever-watchful Rush seized on a poor back pass from West Ham defender Tony Gale, took the ball past goalkeeper Ludek Miklosko and rolled it into the net.
Rush had been uncharacteristically sluggish after 31 minutes when Don Hutchison found him just a few yards out but he failed to control it and pushed the ball to a relieved Miklosko.
After 65 minutes he had a free header from a Jamie Redknapp cross but put it over the top.
West Ham hade made a dream start with Martin Allen putting them ahead in the first minute.
Trevor Morley headed down for Matt Holmes who put Allen clear to chip over the advancing David James.
Liverpool were back on terms after 14 minutes when Steve Nicol crossed to the far post, John Barnes put it back inside and Robbie Fowler drove home.
After that there were three chances at both ends, with James saving from former Liverpool defender David Burrows and a Barnes effort that Miklosko dropped but managed to gather at the second attempt.
But Rush timed it just right for Liverpool - and Hutchison should have made it 3-1 in injury time but allowed Burrows to get back and block his effort.
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