The English Premier League (EPL) club completed their ICC commitments against the Spanish giants, and manager Jurgen Klopp's team treated the sell-out crowd to an exciting, fluent display.
The impressive Mane opened the scoring after a quarter of an hour with an excellent finish after Adam Lallana and Roberto Firmino had linked up well.
Liverpool stormed out of the blocks in the second half and were 3-0 up by the 49th minute thanks to an own goal from former Red Javier Mascherano and a typically classy finish from Divock Origi, Liverpool's official website reported.
Marko Grujic added further gloss to the scoreline with a brilliant looping header in injury time, and Klopp is sure to be satisfied with an encouraging performance and result against a true heavyweight of European football with Liverpool's EPL opener at Arsenal now just eight days away.
But the Reds did not have to wait long to take the lead as Mane rounded off an excellent team move 15 minutes in.
Lallana pickpocketed Juan Camara deep in his own half and broke forward, played a neat one-two with Firmino and then fed Mane, who finished with aplomb, high into Marc-Andre ter Stegen's net from close range.
Messi's effort appeared to spark Luis Enrique's side into life, and Mignolet was called into action shortly before the half-hour mark. The Belgian made a sharp save from Arda Turan's deflected effort before the Turkish midfielder put the rebound wide.
Philippe Coutinho then curled an effort wide after shrugging off the attentions of Aleix Vidal and Mignolet denied Suarez as an entertaining, end-to-end first half came to an end.
Klopp's side flew out of the traps after the break and put the result beyond doubt with two quickfire goals early in the second half.
First, former Red Mascherano could only divert the ball into his own net under pressure from Jordan Henderson after Mane had again got to the byline superbly, and Liverpool were three to the good a minute later when substitute Origi finished coolly after being played in by Kevin Stewart.
Barca were finding it impossible to contain Mane and the Senagalese shot wide after some dazzling footwork before Grujic rounded off the win with a clever header from Lazar Markovic's cross.
Liverpool now fly to Germany on a high for their final pre-season game against Klopp's former club Mainz on Sunday.