Napoli ruins Ranieri's Roma return
Ranieri was appointed Roma boss over the international break, with the 73-year-old coming out of retirement to take charge of the club for a third time.
Yet it was former Roma striker Lukaku who decided this contest at Stadio Diego Armando Maradona, with his 54th-minute effort sending Antonio Conte's team back to the top of Serie A.
Lukaku was well-placed to convert from Giovanni Di Lorenzo's cutback, bringing up his fifth Serie A goal of the campaign.
Roma, which had just two attempts and managed only 0.07 expected goals (xG) in the first half, woke up after Lukaku's goal, with Artem Dovbyk powering a header off the woodwork from a free-kick minutes later, but the visitors' comeback attempts proved fruitless.
Ranieri's next task is to rally his troops for a UEFA Europa League clash with Tottenham Hotspur, fresh off its 4-0 thrashing of Premier League defending champion Manchester City, next week.
There was no sign of an immediate upturn for 12th-place Roma, if it was hoping for a new-coach bounce.
Roma ended the first half with fewer than 70 successful passes (68). It is the first time it has had so few successful passes in the opening half of a league game since 2004-2005.
With only three wins to its name in the league, it has won fewer than four matches in its opening 13 Serie A games for the first time since the 1978-1979 campaign (also three).
Napoli, meanwhile, needed to get back to winning ways after a draw against Inter and a 3-0 loss to Atalanta before the international break, and Conte insists his team must sharpen up.
"Before the match, I told the lads not to look at the table, but to focus on ourselves and improving what we are working on," Conte said.
"I maintain that now too because we need to take a series of steps to raise the level.
"I was satisfied with the performance for a good 65 minutes today, we could’ve taken more of our chances and were up against a strong Roma who have great players.
"Roma were also making their debut under a new coach and therefore were very eager to prove themselves, but we still should've dealt with the final 15-20 minutes better, as we sat too deep and made it complicated for ourselves."
Ranieri acknowledged he has work to do, but tried to remain positive given Roma's poor start to the season.
"If we look back, we have some problems and that is why I was called. We were up against a team that is fighting to win the Scudetto," he said.
"Having said all of that, I am happy with the performance from my players. We made some mistakes that we will talk about during the week, but the hunger, the determination to get back on track was there.
"We have a lot of work to do, but I feel positive.
"We know there is work to be done, we have to focus on reacting rather than sitting there feeling sorry for ourselves.
"The [players] need the right character to help themselves and then others. Naturally, when I arrived, the team was a little closed up, but I think we started to open up a bit by the second half."
Romelu Menama Lukaku Bolingoli
SSC Napoli