Victory saw Jose Mourinho's men close to within two points of top spot in the Premier League with two games to play.
However, third-placed Manchester City will be just three points off the summit, with a game in hand on both Liverpool and Chelsea, if they win away to Crystal Palace later on Sunday.
Senegal striker Demba Ba put Chelsea ahead in first-half stoppage-time when a slip by Liverpool captain Steven Gerrard allowed him to charge through and beat Reds goalkeeper Simon Mignolet in a one-on-one.
Chelsea put the result beyond doubt in added-on time at the end of the match when, with the hosts pressing for an equaliser, former Liverpool striker Fernando Torres led a counter-attack before squaring the ball to substitute Willian for a simple finish.
Chelsea face Atletico Madrid in the second leg of a Champions League semi-final at Stamford Bridge on Wednesday after a goalless initial encounter in Spain.