The friendly, held behind closed doors at Melwood, was arranged by Jurgen Klopp for players not taking part in this week's internationals.
Roberto Firmino scored the Reds' other goal in the 3-2 win.
LFC team: George, Alexander-Arnold, Toure, Lovren, Moreno, Lucas, Allan, Teixeira, Coutinho, Firmino, Sinclair. Subs used: Woodburn, Ojo, Dunn, Whelan, Ejaria, Canos, Kane.