It was only when Frank Lampard was sent off for a dangerous tackle on Xabi Alonso that Liverpool were able to break the deadlock.
With the addition of Ryan Babel and Yossi Benayoun, the Reds looked more threatening in the dying minutes.
With two minutes remaining Fernando Torres scored from a header at the near post to put the Reds ahead. A second in injury time sealed the victory and the valuable three points.
The win puts Liverpool two points behind Manchester United, albeit having played one game more.