A freak goal by Bobby Zamora gave the visitors the lead in the first half, when his cross curled into the near post, beating Pepe Reina who was expecting a corner.
But the Reds dominated the game and turned it around with goals from Daniel Agger and Peter Crouch just before half-time.
Craig Bellamy had a goal disallowed for offside in the second half and the Reds were unlucky not to score more as they controlled the game.
New signing Dirk Kuyt made an appearance to rapturous applause from the Anfield faithful, and was in impressive form.