An own goal from Grant Hanley after seven minutes broke the deadlock before goals from Mohamed Salah, Virgil van Dijk and Divock Origi put the Reds 4-0 up at half-time.
Teemu Pukki grabbed a consolation for the newly-promoted Canaries in the 64th minute as Jürgen Klopp's men now turn their attention towards Wednesday's UEFA Super Cup with Chelsea.
There was also a debut for goalkeeper Adrian when the summer signing came on to replace the injured Alisson Becker with 38 minutes on the clock.
Team news
Jürgen Klopp fielded an unchanged line-up from the Community Shield with Manchester City at Wembley last weekend.