The Brazil international has trained with his new club teammates over the past week following his post-World Cup break and was picked in Jurgen Klopp's starting XI alongside compatriot Roberto Firmino.
Despite faced with formidable opponents who pushed Juventus all the way in last season's Serie A title race, Liverpool were dominant from the off and opened the scoring after just four minutes as James Milner latched on to Sadio Mane's cutback and curled an effort into the top-left corner of the Napoli net.
The Merseysiders then added a second before the 10-minute mark, Partenopei goalkeeper Orestis Karnezis miscuing an attempt to gather Milner's cross in the six-yard box and allowing Georginio Wijnaldum to head the ball into an empty net.
Although Napoli improved as the game went on and even had a seemingly legitimate goal by Jose Callejon chalked off for offside late in the half, Liverpool weathered the storm and soon added a third to their tally just before the hour.
Mane won a challenge with Raul Albiol and worked the ball to Mohamed Salah, who up until then had been largely anonymous, and curled an excellent shot into the far top corner to truly take the wind out of Napoli's sails.
Liverpool were in cruise control from then on and made the most out of a beleaguered Napoli side by launching wave after wave of attacks and finding the back of the net twice more.
Daniel Sturridge weighed in with three chances in quick succession midway through the second half and came up trumps with the third, pouncing on the rebound to stab home on 73 minutes after Divock Origi had stung the palms of Karnezis.
Five minutes later the Reds made it five, Alberto Moreno skilfully going outside his marker, charging into the box and lashing a ferocious effort beyond the reach of the Napoli stopper to cap off a superb performance by the Premier League giants.
LIVERPOOL (4-3-3): Alisson; Clyne (Sturridge 62'), Gomez (Phillips 76'), Van Dijk, Robertson (Alexander-Arnold 62'); Milner (Fabinho 56'), Wijnaldum (Jones 62'), Keita (Origi 71'); Salah (Sturridge 62'), Firmino (Shaqiri 45'), Mane (Solanke 62')
NAPOLI (4-3-3): Karnezis; Hysaj, Albiol (Maksimovic 59'), Koulibaly (Chiriches 71'), Luperto (Rui 45'); Allan, Hamsik (Ounas 63'), Ruiz; (Rog 62') Callejon (Verdi 63'), Milik (Inglese 62'), Insigne (Diawara 63')