Napoli were favourites heading into the away clash against Cagliari, who sit five points above the relegation zone, but they were pushed onto the back foot in the early stages of the contest.
Leonardo Pavoletti almost nabbed a rebound goal after picking the ball up from the edge of the danger area, but he ended up sending his shot over the crossbar.
Napoli managed to swing the momentum in their direction when Callejon drilled the ball into the bottom-left corner just before the half-hour mark.
The visiting side doubled their lead before the half-time whistle blew thanks to Mertens, who controlled the ball in the middle of the box before directing it past the goalkeeper.
The clash continued to be smooth sailing for Napoli in the second half as Hamsik was next to get on the scoresheet after finding himself one on one with the keeper.
The 30-year-old midfielder kept his cool and managed to send the ball into the bottom-left corner with a thumping drive, putting his side into cruise control.
Matters got worse for Cagliari in the 71st minute when the referee pointed to the penalty spot following a handball from Leandro Castan, and Insigne made no mistake by beating Alessio Cragno to give Napoli a fourth goal.
Right at the death, Sarri's side caused even more damage to their opponents as Rui joined the party and got on the scoresheet with a curling free kick from the edge of the box.
The evening was one to forget for the hosts, who have won just seven of their 26 league games this season, while Napoli continue to fly high with three wins on the bounce in all competitions.
CAGLIARI (3-4-2-1): Cragno; Castan, Ceppitelli, Romagna; Lykogiannis, Padoin (Ionita 59'), Barella (Deiola 77'), Farago; Joao Pedro; Pavoletti, Han (Cossu 62')
NAPOLI (4-3-3): Reina; Rui, Koulibaly, Albiol, Hysaj (Maggio 74'); Hamsik, Jorginho (Diawara 75'), Allan; Insigne, Mertens (Zielinski 42'), Callejon