Goals from Daniel Sturridge, Alberto Moreno and Roberto Firmino put Jurgen Klopp's men firmly in charge in an excellent first-half display.
A much-changed Reds XI could not match the intensity after the break, and they did not add further to the score despite a number of chances, notably from Adam Lallana and 17-year-old Ben Woodburn.
However, it was still a comfortable victory for Liverpool, and a chance for some old faces to pull on the red shirt once again.
Both clubs provided their lineups ahead of kick-off:
Liverpool were on the scoresheet in no time. Sturridge drove into the box from the right edge in the eighth minute and, after a neat piece of footwork, buried a finish into the far corner.
Ten minutes later Moreno doubled the visitors' lead, finishing powerfully from 15 yards after controlling a fine chipped ball from Firmino with his first touch.
The Brazilian himself then got in on the act six minutes before the break, poking home from close range after more excellent work from Sturridge on the right.
It was a slick and fluid opening 45 minutes from Liverpool, and they arguably deserved to be up by more.
Just before the break Liverpool had decent shouts for two penalties, first after Sturridge was felled in the area by Sebastian Ryall, and then when Gerrard looked to have been pushed by Brandon O'Neill.
Neither were given, and Klopp was not happy with the referee at half-time, per James Pearce of the Liverpool Echo:
Seven changes were made at the break for the Reds, with Carragher and Gerrard both being taken off, as well as Sturridge.
Carragher took to Twitter to provide an analysis of his performance:
Sydney enjoyed a better time of things after the break. They continued to concede chances to Liverpool but looked more capable of netting themselves against a much-changed Reds side, which also included Daniel Agger.
Simon Mignolet was forced into a fine save from O'Neill's effort 10 minutes from time to ensure Liverpool kept a clean sheet.
And Trent Alexander-Arnold was denied a glorious goal to finish the game off in the final minute when his rasping effort from 20 yards rattled the post.