The performance seldom hit the emphatic heights of the weekend's 5-0 thrashing of Napoli and suffered something of a false start when new signing Fabinho swiped a penalty wide after Gleison Bremer tripped Sadio Mane.
It mattered little as Roberto Firmino opened the scoring with a deflected effort in the 21st minute after Mohamed Salah slalomed across the field.
Firmino then turned provider, sliding a pass through for Georginio Wijnaldum to slam home but Andrea Belotti headed the visitor back into the contest after the half hour.
There had been wholesale changes – including Loris Karius replacing Alisson on the latter's maiden Anfield appearance – and two substitutes combined to make sure of victory.
Xherdan Shaqiri brought down a raking ball and exchanged possession with Nathaniel Clyne before floating in a cross for Daniel Sturridge to nod in.
Jurgen Klopp's men begin their Premier League campaign against West Ham.