Goals from Goran Pandev, Gokhan Inler, Jose Callejon and Marek Hamsik ensured that the Partenopei stayed on track behind Serie A leader Roma.
The Tuscany-based visitors were no match for Rafa Benitez's men, and goals from Goran Pandev, Gokhan Inler, Jose Callejon and Marek Hamsik spread throughout the game ensured all three points went the Partenopei's way.
The likes of Gonzalo Higuain, Christian Maggio and Raul Albiol were unavailable for selection due to injury, but that did not stop the hosts getting off to an ideal start as Pandev punished the Amaranto on the counterattack by lashing in past Francesco Bardi within four minutes.
At the other end, Pasquale Schiattarella and Innocent Emeghara came close to pulling the game level before Pandev nearly doubled the lead - and his tally - but could not keep his effort beneath the crossbar.
On 26 minutes, however, Benitez's men were able to extend the difference to 2-0 and Livorno goalkeeper Bardi was arguably to blame, as he was unable to parry Inler's long-range effort over the woodwork.
Emeghara again went close as Livorno attempted to fashion a fightback, his volley thundering off the crossbar with Pepe Reina beaten and halftime imminent.
Usual service resumed after the break as ex-Real Madrid attacker Callejon, one of Napoli's many summer signings, added a third for the hosts, defeating Bardi with a low, deflected shot on 54 minutes.
Victory for the Naples side was an inevitability as the game wound to a close, though a brilliant save from Bardi kept Dries Merten's off the scoresheet as his fine free kick looked destined to rustle the back of the net.
But Napoli finally grabbed its fourth and final goal with seven minutes left on the clock, as Lorenzo Insigne saw his shot saved before playmaker Hamsik thumped in the rebound to score his fifth goal of the Serie A campaign.