The 25-year-old, who continues to be linked with a move to Barcelona, made the third goal with a lofted ball through for Mohamed Salah to score.
Salah's fellow summer signing Dominic Solanke headed in the opener, with Georginio Wijnaldum also on target.
"Coutinho and Salah are two top level players, and we are extremely happy to have them," said manager Jurgen Klopp.
"We are not quite where we want to be, but that is normal in pre-season."
Philippe Coutinho captained Liverpool as they beat Hertha Berlin 3-0 in their latest pre-season friendly.