Lorenzo Insigne, Arkadiusz Milik and Amin Younes scored the goals for the Serie A side in front of a sell-out 65,442 crowd in Edinburgh.
There were, at least, more minutes in the bank as Jürgen Klopp used 21 players over the course of the contest, a week before the campaign begins with a trip to Wembley for the Community Shield.
Liverpool – and Andy Robertson, on home soil – created the first chance of the half.
It was the Scotland captain’s fourth-minute delivery from the left that found Divock Origi, unmarked but with his back to goal, and the No.