New signings Diego Cavalieri and Philipp Degen were introduced at the break.
Tranmere had their new names - John Curtis, George O'Callaghan, Bas Savage and Edrissa Sonko on show - but it was the expected better passing, movement and control of the Liverpool outfit that had them very much in control.
Reds boss Rafa Benitez said: "I was delighted with the fitness levels of the players, Benayoun scored a fantastic goal and there were plenty of things that were really positive.
"I was happy with Daniel Agger's comeback, he will be a welcome addition to our defence in the coming season.
"Philipp Degen also did well on his debut, he was very impressive attacking down the right side."