Youngsters Stephen Darby, Jack Hobbs, Damien Plessis, goalkeeper David Martin and Emiliano Insua all had run-outs.
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.
Martin had to save well from Chris Greenacre, but former Wales international Danny Coyne kept the score down until Benayoun's 20-yarder saw Liverpool ahead.
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."