Pool had gone 2-0 before the break, though Joel Matip clawed one back to make it 2-1 prior to the half-time whistle.
It stunned Jurgen Klopp into some much-needed changes at the break after a disappointing showing.
Billy Koumetio, making his debut for the Reds, was at fault for the opening goal after he lost the ball in defence.
The 17-year-old had stepped up at centre-back but his error saw CJ Hamilton score first.
And there were more problems at the back after a rash decision from Alisson saw him give away a penalty, which was tucked away by Jerry Yates after half an hour.
Matip's goal saw Liverpool get one back before they turned on the style in the second half.
The Reds goalscorer was hauled off for Nat Phillips, while Koumetio and Fabinho were also subbed off for Sepp van den Berg and Curtis Jones.
It did not take long for Liverpool to equalise with Sadio Mane, who scrambled one over the lines.
And just minutes later his strike partner Roberto Firmino struck with a cheeky backheel effort to take the Reds into the lead.
The floodgates were then opened to the Merseyside outfit, who went on to score a further four times.
Harvey Elliott, Takumi Minamino, Divock Origi and Van den Berg later struck to make it 7-2 and a reasonably comfortable afternoon for Klopp in the end.
Klopp has signed just one player this summer, Kostas Tsimakis from Olympiakos.
The Greece international will provide competition at left-back, but there are further pursuits planned for the likes of Thiago Alcantara and Kristoffer Ajer.