Goals from Luis Alberto, Iago Aspas, Martin Kelly and Raheem Sterling were more than enough for victory but Giancarlo Gonzalez did become the first man to score against the Reds this summer.
The Reds, who were without wantaway striker Luis Suarez, took the lead as Aspas' delicate chip came back off the bar and an attempted clearing header only went as far as Alberto who hit a crisp volley into the bottom corner.
But the lead lasted just four minutes as Gonzalez got across Jordan Henderson on the edge of the six-yard box and headed home.
Brendan Rodgers' side were back in the lead a minute before the break as Stewart Downing hit the byline and threaded the ball to Aspas in the box who netted his fourth goal of pre-season.
And the lead was doubled nine minutes into the second half as Kelly found the net with the faintest of touches after a corner had caused confusion in the home penalty area.
Kolo Toure hit the bar with a header moments later and Fabio Borini was close to finding the net from a narrow angle but could only fire past the far post.
There was still time for Borini to hit the bar with a crunching effort before Sterling finished off a slick move involving Philippe Coutinho and Oussama Assaidi to seal an emphatic win.