Bluebirds boss Neil Warnock stuck with the same starting XI which began the crucial 2-0 victory at fellow strugglers Brighton on Tuesday evening.
Meanwhile, the Reds handed recalls to Jordan Henderson, Naby Keita and Roberto Firmino, with James Milner, Fabinho and Divock Origi all dropping to the bench.
The visitors started brightly in the South Wales sunshine, with the hosts unable to make any headway in the attacking third, before Nathaniel Mendez-Laing started to find space to use his pace on the left flank.
Twenty-two minutes in Firmino passed up a huge chance to open the scoring as he was played in by Sadio Mane, with the Brazilian unable to hit the target from 12 yards out when he should have done much better.
On the half-hour mark Mane flicked a near-post effort over the top, as he met an accurate ball in from the right from Trent Alexander-Arnold.
City keeper Neil Etheridge then made a decent save to block a Mo Salah shot, while at the other end Alisson Becker was finally forced into action to turn over an acrobatic effort from Oumar Niasse.
The Bluebirds threatened from a couple of long balls into the area early on in the second half, before the Reds sprang forward and Mane curled an effort narrowly over the crossbar.
Alexander-Arnold then flashed a long-range effort wide before the Reds made the breakthrough 11 minutes into the second half, with the England full-back scuffing a corner right into the path of Georginio Wijnaldum, who lashed home a superb half-volley.
Jordan Henderson spurned a chance to double the lead as he shot well over when well placed inside the area.
The home fans were then left holding their heads in their hands as Sean Morrison somehow failed to head home from close range, after a corner curled over from the right cleared everyone at the near post, including Reds keeper Alisson.
City continued to show ambition to try and rescue something from the game, but were undone nine minutes from time as Morrison was adjudged to have held back Salah and sub Milner rifled the resulting spot-kick into the corner of the net, sending Etheridge the wrong way.