New signing Luis Diaz was named on the bench and reserve goalkeeper Caoimhin Kelleher started ahead of Alisson Becker who just returned from national team duty.
Liverpool looked to settle first through an early chance by Diogo Jota, but the former Wolves man was smothered by Dillon Phillips.
Jurgen Klopp's men maintained the momentum towards the last 20 minutes of the half and should've been ahead from a one-two in the area, but Curtis Jones squandered.
However, the Reds didn't put their earlier work to waste eight minutes in the second half after Jota glanced at a delivery from Trent Alexander-Arnold to head home.
Liverpool looked to add a second just after two minutes through the head of Roberto Firmino from a ball in by Konstantinos Tsimikas, but he didn't trouble Phillips.
Then, it was time for the Reds to put on fresh faces towards the midway point of the second period in Harvey Elliott for Naby Keita and withdrew Jones for the new boy Diaz.
The latter's introduction proved telling as he nicked a ball into space for Jota 68 minutes in who then allowed Takumi Minamino to get a look in and prod in their second.
There was more to come for the Reds after Elliott controlled a ball into the area eight minutes apart from Andrew Robertson to volley into the back of the net.
Cardiff reduced the home side's advantage ten minutes to fulltime when Rubin Colwill raced forward following a move on the edge of the area and curled beyond Kelleher.
The Reds controlled the final stages of the match as Cardiff targeted a turnaround to set up a round five date with Norwich City.