Antonio Conte was hired in July and now they are ending 2024 level with Atalanta atop the Italian league again.
Substitute Giacomo Raspadori scored a late goal and Napoli beat relegation-threatened Venezia 1-0 in their final match of the year.
Napoli trail Atalanta only on goal difference but both teams are one point ahead of defending champions Inter Milan, who have a game in hand.
"Even if I play cards with my daughter I want to win," said Conte, who was hired to get Napoli back into the Champions League.
"Personally, I don't accept minimal goals. But we all know where we started and what the club's objectives are.
"The squad is improving under every point of view. We just need to score more goals."
Napoli had struggled to get the ball past Venezia goalkeeper Filip Stankovic, the son of former Lazio and Inter standout Dejan Stankovic. But Raspadori broke the deadlock in the 79th minute when he used one touch to fire in a loose ball from the centre of the area less than 10 minutes after he came on.
"These are tough matches where it means a lot to come away with three points," Raspadori said.
"We know we're on the right path."
In the first half, Stankovic saved a penalty kick from Romelu Lukaku. Then in the second half Stankovic deflected a Lukaku effort off the post, one of 25 Napoli shots to Venezia's four.
Also on Sunday, Juventus and Fiorentina drew 2-2 in a match that was briefly suspended because of discriminatory chants aimed at Juventus striker Dusan Vlahovic.
Vlahovic, a Serbia international who played for Fiore before transferring to Juve three years ago, appeared to tell the referee about the chants. The ref then stopped play, gathered the teams and ordered a warning announcement to be made over the stadium's public address system.
Juventus, the only unbeaten team in the league who have drawn more matches (11) than they've won (seven), and Fiorentina are both nine points behind the leaders.
Elsewhere, AC Milan and Roma drew 1-1 at the San Siro and Torino came back from two goals down to draw 2-2 at Udinese.