The South American strike partnership combined to great effect as the Italians seized the initiative in the first knockout round, with both teams exploiting defensive errors
Juan Mata opened the scoring after 27 minutes when an error from Paolo Cannavaro let him in for an easy finish, but Lavezzi hit a classy equaliser on the edge of the area shortly afterwards.
Cavani raced past a ball-watching Branislav Ivanovic to bundle home with his shoulder just before half-time, with Lavezzi deepening the visitors' woes midway through the second period as a result of a calamitous David Luiz mistake.
The hosts boasted a full-strength front line with Blues target Cavani leading the attack alongside Marek Hamsik and Lavezzi.
Andre Villas-Boas, meanwhile, boldly dropped Fernando Torres and Frank Lampard to the bench, while Ashley Cole was also among the substitutes in favour of Jose Bosingwa. Didier Drogba returned to the starting line-up after the Africa Cup of Nations but captain John Terry missed out ahead of having surgery on Wednesday for a knee problem.
Napoli started well, with Petr Cech called into action early when Cavani evaded Gary Cahill in the box to shoot with venom before the Blues goalkeeper saved well with his foot.
Moments later Hamsik fed Christian Maggio on the right flank. The wing-back burst into the area and drew a fine fingertip save from Cech.
Chelsea, though, found a breakthrough in the 27th minute. Throwing large numbers forward, they put home skipper Cannavaro under pressure and the defender miskicked as he tried to clear Daniel Sturridge’s pass. He succeeded only in playing in Mata, who exuded coolness with a simple side-footed finish.
Napoli, however, got back on level terms just over five minutes before the break. Cavani, on the turn, played it square for Lavezzi on the edge of the area. The Argentine had no trouble moving past Meireles before curling the ball into the bottom corner with a sublime right-footed finish.
Chelsea came forward immediately after the kick-off, Ramires advancing unchallenged through the middle, inexplicably allowed sight of goal, but the Brazilian blasted his effort well over.
Just as it seemed that the visitors would reach half-time on equal standing, Cavani was allowed to get past Ivanovic as they raced to meet a cross from deep on the right. The Uruguayan reached the back post and threw his shoulder against the delivery, doing enough to divert it into the net and secure a lead at the break.
Napoli started the second half looking to counter and should have extended their lead when Cavani, leading a break through the Chelsea lines, set Lavezzi up with a through-ball on the inside-left channel after Cahill moved out of position, but the Argentine dragged his effort too far wide.
The Blues were dominating the half but Luiz made a horrendous mistake at its midway point, attempting to deal with an innocuous long pass forward from Campagnaro by flicking it away with flair but succeeding only in surrendering it to Cavani, who once again passed square to Lavezzi. The forward dispatched it with ease to earn his side a two-goal cushion.
Villas-Boas looked to wrestle back control by summoning Lampard and Essien from the bench but chances dried up at both ends for a period as Chelsea were visibly affected by conceding the third.
They were lucky not to see a fourth go past them when, with 10 minutes to go, Cavani held the ball up on the edge of the Blues’ area before laying it off to Hamsik, who controlled and swivelled past a defender before playing it across for the waiting Maggio. The right-back tried to sweep it in but Cole kept it out on the line, though the Italian should have taken him out of the equation.
Chelsea laboured late in search of another away goal, Lampard hitting a testing long shot into De Sanctis' arms in stoppage time, but it ended with Napoli in control of the tie.