Two superb first-half goals by Dirk Kuyt and Jermaine Pennant handed the hosts the important victory at Anfield.
Liverpool are now just six points behind the champions.
Manchester United have a chance of stretching their lead in the Premiership to nine points, if they manage to win over Arsenal at the Emirates tomorrow.
There was even more bad news for Chelsea today, when Dutch winger Arjen Robben hobbled off the pitch, with something that appeared to be a hamsting injury.
