Cavani, who hadn't scored since October 29, gave Napoli the lead with a glancing header off a corner in the 17th minute. Italy forward Mario Balotelli then took advantage of a defensive error to equalize for City in the 33rd. But Cavani restored Napoli's lead in the 49th, taking a cross from Andrea Dossena and firing past goalkeeper Joe Hart from the center of the area. In a furious finish, Napoli forward Marek Hamsik hit the post in the 76th and Balotelli wasted four chances to equalize.
Bayern Munich lead Group A with 13 points after beating Villarreal 3-1. Napoli are next with eight, City seven and Villarreal zero.
Getty Images
In the final group round on December 7, City host Bayern and Napoli
visit Villarreal. Napoli control their own destiny, and can advance by
winning their final match no matter what City do.
"We still haven't done anything," said Napoli manager Walter Mazzarri. "We've got to go beat Villarreal in Spain, and don't think that's going to be easy. But let's enjoy this for now. Advancing in this group would be a real achievement. You've got to remember that Napoli haven't won matches at this level for 21 years."
City need to beat Bayern and hope Napoli don't win in Spain.
"You never know. We'll see what happens," said Roberto Mancini, City's Italian manager manager. "We didn't deserve to lose, but in the Champions League you can't allow your opponents certain types of chances. Napoli are a sneaky Italian side. We had our chances and it just didn't go in."
"I'm upset over the result but not anything else. I was pleased with our performance. But we conceded two goals that we shouldn't have allowed."
Mancini said there was "no explanation" for the difference between City's results in the Premier League - having beaten Manchester United 6-1 last month - and in Europe.
"This is a strong unit that plays good football and plays to win but occasionally you can lose matches, especially in the Champions League," he said. "I'm not angry and I'm not disappointed. This can help us grow."
For Cavani's first goal, the ball also touched City defender Aleksandar Kolarov and Hart before going in, and Cavani nearly scored again when he hit the side of the net two minutes later.
Cavani scored 26 goals for Napoli in Serie A last season, managed a hat-trick against AC Milan in September and also found the net in his opening two Champions League games this season. But he had struggled in recent weeks, with his last goal coming against Catania in the Italian league last month.
"Let's enjoy this beautiful moment. We knew we could do it from the very first day," Cavani said. "We always prepare to give our maximum and today we were at our best."
City's equalizer was the product of a poor clearing attempt from Salvatore Aronica. The ball went directly to David Silva, whose shot was deflected by goalkeeper Morgan De Sanctis directly to Balotelli, who sent it into an empty net.
"(Aronica) made a mistake but otherwise he played great," Mazzarri said. "You've got to remember that most of this squad is playing the Champions League for the first time and this was only our fifth match."
Balotelli was playing his first club match back in his home country since leaving Inter Milan and he now has two Champions League goals to go with his six Premier League scores this campaign.
Mancini revealed that Balotelli had a fever on Monday, but said he felt better before the match.
The scene at the San Paolo stadium was electric, with about 60,000 fans filling the stands for one of the biggest crowds since Diego Maradona led Napoli to Italian titles in 1987 and 1990.
However, there were only a couple of thousand City fans, leaving the visiting supporters cage - which features double sets of Plexiglass barriers and netting stretching up to the stadium roof - half empty.
Before kick-off, Napoli fans put on a fancy display, as fans held up cards in the squad's blue-and-white colors nearly all the way around the main ring of stands, and formed the outline of the letter 'N' with lines of flares on one end.
During the second half, fans held aloft a banner mourning the recent death of Maradona's mother, Dalma Salvadora Franco de Maradona. It read, "Lay in peace the mother of football, ciao Dona Tota."
City began with Balotelli and Edin Dzeko in attack - leaving Sergio Aguero, their most productive scorer this season and Maradona's son-in-law, on the bench. Aguero came on for the final nine minutes.
Napoli countered with their "Three Tenors" of Hamsik, Ezequiel Lavezzi and Cavani.
In the 63rd, Balotelli couldn't quite reach a cross with only the goalkeeper to beat, and he then was denied by De Sanctis in the 78th, headed high in the 82nd and failed to redirect a corner in the 84th.
After the final whistle, fans stayed inside the stadium to sing along to the old Neapolitan folk song, "O surdato 'nnammurato," while fans elsewhere in the city poured out onto the streets and celebrated with fireworks.