A first half double from Steve Gerrard and a late strike from Babel keeps the pressure on Manchester United, who face city rivals Manchester City on Sunday.
Liverpool stormed into the lead after just 78 seconds when Gerrard latched onto a through ball from Torres and easily rounded Hammers keeper Robert Green to open the scoring.
The lead was doubled in the 38th minute when Luis Boa Morte tugged at the jersey of Fernando Torres, and referee Alan Wiley had no hesitation in pointing to the spot. Green saved the Liverpool captain's initial effort, but Gerrard was not to be denied, reacting first to the breaking ball and stroking it into the net.
Babel, on as sub in the second half, scored a third in the 84th minute to make it 3-0. The Dutch winger had his initial header saved after a good cross from Kuyt, but he easily dispatched the rebound to cap an easy win for the Merseysiders.
Liverpool are top of the table tonight on goal difference, but United have two games in hand with fixtures running out.