The South American pair made the difference in a match where the visitors had taken the lead through Juan Mata before squandering two more chances and putting under-fire manager Andre Villas-Boas under yet more pressure.
Lavezzi scored Napoli's first and third goals, the first of the competition for the Argentine and both laid on by Cavani who notched the other himself.
The prolific Uruguayan took his tally to six in the Champions League and 19 in his last seven outings.
Napoli's win left England in danger of missing out on the quarter-finals after Arsenal, the Premier League's only other team in the last 16, were thumped 4-0 at AC Milan last week.
It also left Villas-Boas facing more questions about his future as the poor run of form continued for the London team, who have won only two of their last 10 Premier League games and who drew against second tier opponents in the FA Cup last weekend.
Asked if he expected to be in charge by the time his side host Napoli for the return leg on March 14, the Portuguese told Sky Sports: "Yeah, for sure."
Chelsea's day had got off to a bad start with news that captain John Terry could be sidelined for several weeks after aggravating a knee injury and it soon got worse.
"After the first goal, we missed opportunities to go 2-0 up and then we should have defended better but we made a couple of mistakes against Napoli with their attack you are going to get punished," said Villas-Boas.
"I think the third goal was perfectly avoidable... we can create problems with our attacking options and we created problems [for them] today.
"It is a game of efficiency and Napoli had it. I think the statistics are very similar for both teams. Both teams created a lot. The game was open."
Napoli were missing coach Walter Mazzarri who was banned for both legs after he was sent off for pushing Villarreal forward Nilmar in a group match, a move he said was intended to galvanise his team.
They were fired up enough without him, although Lavezzi refused to get carried away, saying: "I was happy to score but the important thing was that the team won. We haven't qualified yet."
UNBEATEN RECORD
Napoli, unbeaten at home since returning to European competition in 2008 following a 13-year absence, were quickly on the attack and goalkeeper Petr Cech twice prevented Chelsea from shipping an early goal.
He saved a dangerous Cavani shot with his foot and then turned Christian Maggio's angled effort around the post as the Italians quickly showed their attacking potential with fast, pinpoint passing.
But the visitors went ahead with their first real chance after Napoli captain Paolo Cannavaro sliced Daniel Sturridge's cross and the ball fell at the feet of Mata, who beat Morgan De Sanctis with a first-time shot
Brazilians David Luiz and Ramires went close for Chelsea as the usually passionate Sao Paolo stadium went eerily quiet.
Luiz beat De Sanctis to a corner but his header just cleared the bar while Ramires fired over from the edge of the area.
The crowd came back to life in the 38th minute when Cavani fed Lavezzi on the edge of the area and he curled a delightful shot inside the near post, although the Chelsea defenders allowed him too much space for the shot.
Chelsea's rearguard got into another mess in first-half added-time as Gokhan Inlan delivered a teasing cross which bounced six metres from goal and Cavani stole in front of two defenders to fire Napoli in front with his shoulder.
The visitors started the second half brightly with Florent Malouda having a shot saved by De Sanctis and Didier Drogba just failing to take
