Rafael Benitez picked the same eleven that started against Besiktas on Tuesday and they started the game brightly with Sami Hyypia forcing an early save out of Niemi with a 20 yard drive. The Finn then headed narrowly over after a cross from Alvaro Arbeloa.
Steven Gerrard had the Reds' next chance when he received the ball on the edge of the 18 yard box but he lifted the ball over the bar and into the Anfield Road end.
Fulham's only real chance of the half fell to former Red Danny Murphy when he volleyed at goal but Pepe Reina was never troubled by the shot.
Liverpool's best chance of the half came in the 45th minute. Peter Crouch jumped highest to meet a Gerrard free kick but his header came back off the woodwork with Niemi beaten.
The Reds raised their game after the break and it became one way traffic towards the Fulham goal. Fabio Aurelio came close with a free kick which Niemi could only palm out. Yossi Benayoun was first to the rebound but he sent that over the bar under pressure from a defender.
Andriy Voronin then had a couple of good chances. First he turned a defender and hammered a shot goalwards that Niemi could only palm over for a corner and then he linked up well with Benayoun only to send his low shot the wrong side of the post.
Subsitute Ryan Babel then found Benayoun in space on the left but the Israeli's fine dipping shot was again palmed over for a corner by the in form Niemi.
Fernando Torres was sent on for the final twenty minutes and it was he who finally broke the deadlock. The Spaniard brought down Pepe Reina's long clearance, cut inside the defender and then slotted home at the near post past the wrong footed goalkeeper.
Steven Gerrard wrapped the game up from the penalty spot five minutes later after Peter Crouch was brought down after running onto Babel's clever through pass.
