Antonio Conte’s Inter ended their 23-year wait for a league win in Naples to stay in pole position, level on points with Juventus after 18 games, but ahead on goal difference.
Lazio are third, six points adrift but with a game in hand, after stretching their winning run in the league to nine matches on Sunday with a 2-1 victory over Brescia.
“It’s an important victory, winning away to Napoli is never easy,” said Conte after his 100th Serie A win as a coach but first in Naples.
“Napoli have in recent years always been behind Juventus, while Inter was a long way back. This year we have reduced the gap.”
Inter’s three goals all came from mistakes from Napoli, runners-up the past two seasons but only eighth this term.
Lukaku broke through on 14 minutes with a powerful solo run through the Napoli defence, with goalkeeper Alex Meret fumbling the second into goal in the 33rd minute.
Polish striker Arkadiusz Milik pulled a goal back for Napoli four minutes before the break.
But Lautaro Martinez added the third after the hour mark, following another mix-up in the Napoli defence, to give Inter their first win at the Stadio San Paolo since October 1997.
“We made lots of mistakes and scored three goals on our own,” said Napoli coach Gennaro Gattuso.
“The lads are worried because they are used to challenging for the Scudetto and this year it’s like this.”
In Turin, Ronaldo struck for the fifth consecutive league game as the champions bounced back from their Italian Super Cup defeat by Lazio.
“Amazing feeling to kick off 2020 with a hat-trick and a victory,” tweeted Ronaldo, who brought his league tally to 13 goals.
Ronaldo, 34, broke the deadlock just after the interval.
The Portuguese striker added a second from the penalty spot on 67 minutes then set up substitute Gonzalo Higuain nine minutes from time, before completing his hat-trick a minute later.
– ‘Like a God’ –
Lukaku and Ronaldo’s goals overshadowed Zlatan Ibrahimovic’s return for AC Milan as the Swedish star came off the bench in the 55th minute in a goalless draw against Sampdoria.
The 38-year-old had not played since leaving MLS side LA Galaxy in October.
He came on for Poland striker Krzysztof Piatek to deafening applause from the San Siro crowd after rejoining the club last week.
But there was little else to cheer for the hosts who extended their winless run to three games and remain 12th in the table.
“I felt a lot of adrenaline, emotion, it brought me back nine or 10 years,” said Ibrahimovic, who was top scorer in Serie A with Milan in the 2011-12 campaign before leaving for Paris Saint-Germain.
“I wanted to get on the pitch, score a goal and then celebrate like a God in front of the Curva! But it will happen next time.”
The seven-time European champions are 13 points off Champions League qualification, a competition they have not played since the 2013-14 season.
– Five-star Atalanta –
Milan coach Stefano Pioli said the team were still reeling from their 5-0 defeat by Atalanta last time out.
“The disastrous defeat in Bergamo has remained within us,” said Pioli. “It is a shame not to have won. Ibra’s impact was absolutely positive.
“He immediately gave support, but the team is not yet used to his presence, we could look to him more.”
Atalanta continued their fine form, closing to within a point of fourth-placed Roma, who lost 2-0 to Torino on Sunday, with another 5-0 rout, this time of seventh-placed Parma.
Atalanta were already three goals up before the break thanks to Papu Gomez, Remo Freuler and Robin Gosens, with Josip Ilicic adding a second-half double.