In a match that saw three own goals and a red card for the visitors' Ian Nolan, Luis Suarez still managed to take at least a few of the headlines by continuing his fine recent scoring form.
The Reds took the lead three minutes before the interval, when Guy Demel deflected a Suarez shot past his own 'keeper.
The advantage was doubled shortly after the break, when the returning Mamadou Sakho netted a second. But an own goal from Martin Skrtel halved the deficit and gave the visitors hope.
That was until Suarez headed in a third and Nolan was dismissed for a poor challenge, leaving Sam Allardyce's men with a mountain to climb.
There was still time for another Suarez strike to deflect in off Joey O'Brien, leaving West Ham only outside the relegation zone on goal-difference while Brendan Rodgers' side remain hot on the heels of leaders Arsenal.