A brace from Luis Suarez and one from Raheem Sterling saw the home side go in at half-time 3-0 to the good. And while the Bluebirds scored the only goal of the second-half, Liverpool ran out comfortable winners.
The Reds had 27 shots to Cardiff's 10, although Brendan Rodgers will not be happy that only seven of those were on target. Liverpool also dominated possession, having 69% of the ball.
Suarez opened the scoring with a volley midway through the first-half. He then set up Sterling for a 42nd-minute tap-in before curling a low shot past David Marshall for the third.
Jordon Mutch headed in for Cardiff, whose defeat will now generate further headlines about the future of manager Malky Mackay. While Liverpool can celebrate being top of the pile, Cardiff will have to make do with being 15th.