The former Real Madrid attacker netted twice to help the hosts to a vital win in the race for Champions League football.
Senad Lulic gave the away side the lead halfway through the first half, but Dries Mertens restored parity shortly before the interval. Lorik Cana was then sent off before Gonzalo Higuain netted a hat trick to help the hosts to victory, with Ogenyi Onazi's late goal serving as little more than a consolation strike.
Napoli started the match with attacking intentions, yet it was the hosts who drew first blood after 20 minutes of play. Stefano Mauri set up Lulic with a fine pass and the midfielder beat Pepe Reina with a superb finish to make it 1-0.
The hosts came close to equalizing shortly after when Goran Pandev reached Higuain, but the Argentine was denied by a superb save from Etrit Berisha.
There was little the Albanian goalkeeper could do about Mertens' equalizer in the 42nd minute, though. The Belgium international collected a Raul Albiol pass before trying his luck from outside the area and left Berisha no chance with his powerful shot.
The former PSV winger again played a big role shortly after the break when he won a penalty after being fouled by Cana, with the latter receiving his second yellow card of the game for his action. Higuain stepped up and had no trouble finding the net from 12 yards.
Things got even worse for Lazio halfway through the second half as Higuain doubled his personal tally to hand Napoli a two-goal lead in the 67th minute. The prolific striker shook off Stefan Radu after being set up by Lorenzo Insigne and kept his calm in front of Berisha to make it 3-1.
Lazio was not giving up, however, and was rewarded for its efforts in the closing stages of the game when Onazi pegged one back, but it was too little too late for the guests. Higuain eventually put the match to bed well into stoppage time with his third goal of the game.
Rafa Benitez's men remain third in Serie A with 67 points from 33 games, while Lazio sits seventh in the league table with 48 points.