The Reds travelled to Dublin for the match against the Italian giants, with both sides showcasing virtually full-strength sides.
Mane stars in dominant first half
James Milner opened the scoring inside of five minutes with a brilliant left-footed drive from the edge of the area, with Sadio Mane providing the assist.
The Senegalese winger set the ball back to the stand-in captain from the six-yard spot, and Milner made no mistake when he lashed home with ease.
Gini Wijnaldum doubled the scoring only five minutes later as he beat Napoli goalkeeper Orestis Karnezis - linked with a £25million move to Anfield prior to the arrival of Alisson - to a cross from a short corner, heading the ball home at the front post.
Sadio Mane looked sharpest for the Reds going forward, constantly on the shoulder of the last defender and liking up brilliantly with his compatriots in the feared front three of Liverpool's forward line.
Roberto Firmino had the ball in the back of the net shortly after when he latched onto a stray back-pass, however, the referee adjudged the ball to have been played by Mo Salah and wrongly ruled the goal out for offside.
Sturridge the stand out in the second half of substitutions
It was the Egyptian Salah who bagged the third goal for Liverpool with a lovely curled effort into the top corner of Napoli's goal, prior to being substituted.
Daniel Sturridge, who replaced Sadio Mane on the hour mark, found the net in the 73rd minute when he latched onto a stray ball on the edge of the area to fire home in what looked like a simple shooting exercise.
Sturridge's goal takes him to a total of five in pre-season, one of the highest hitting summer stats of recent years for Liverpool.
German boss Jurgen Klopp will be hoping to keep the former Chelsea and Manchester City forward fit and firing, with a fresh Sturridge the equivalent of bolstering his forward line even further following the addition of Xherdan Shaqiri.
The Englishman turned provider when he played an inch-perfect ball to Alberto Moreno across the field, who smashed home from close range in emphatic fashion.
The game was rounded off in professional fashion for the Merseysiders, with substitute defender Nathan Phillips putting his body on the line to preserve debutant Alisson's clean sheet for the day.
The Reds will now return to England for their final pre-season game against Torino at Anfield on Tuesday evening.