Manager Villas-Boas has repeatedly insisted his job would not depend on the outcome of the Champions League last-16 tie with Napoli but, despite an improved attacking performance, his players heaped more pressure on him with another defensive horror show.
Having thrown away winning positions countless times both at home and abroad since Villas-Boas took charge, Chelsea did so again to make it five matches without a win.
Their defending for all three Napoli goals was shocking.
A 3-1 win was no more than Champions League surprise package Napoli deserved - despite gifting Juan Mata the opening goal - with their attacking trio wreaking havoc against a defence once again badly missing the leadership of injured captain John Terry.
Villas-Boas may also come under fire for not starting with Frank Lampard or Michael Essien in what is regarded one of the most hostile atmospheres in Europe.
Indeed, the cacophonous Napoli fans, swirling wind and driving rain gave the whole occasion an almost apocalyptic feel.
The visitors were immediately under pressure, Petr Cech needing to be alert to race off his line, while captain-for-the-night Didier Drogba briefly stayed down after a clash of heads.
Both were a prelude for worse to follow in the 10th minute when Cech produced real heroics after Cavani looked certain to convert Ezequiel Lavezzi's pass, the goalkeeper just getting his foot to the ball.
Injury really did then strike when Jose Bosingwa limped off with what looked like a hamstring pull, forcing a half-fit Ashley Cole on far earlier than expected.
More brilliance from Cech denied Christian Maggio from a tight angle but Napoli were looking far from secure at the back themselves and, from nothing, they gifted Chelsea the lead.
Drogba found Daniel Sturridge, whose cross was inexplicably flicked back towards his own goal by Paolo Cannavaro, falling perfectly for Mata to fire left-footed beyond Morgan De Sanctis.
A stunned San Paolo struggled to process what had happened, with the visiting fans finally able to make themselves heard.
They might have been celebrating again when Sturridge wasted a glorious opportunity to play in Mata for goal number two, instead greedily trying to beat his man, while the resultant corner saw David Luiz power a header narrowly over.
Chelsea were in the ascendancy but they allowed Napoli to level seven minutes before half-time, Lavezzi given an age with which to curl a beautiful 25-yard shot beyond Cech.
Ramires should have restored the visitors' lead when the home defence parted in front of him but he blazed over the bar.
Raul Meireles was booked for handball, suspending himself for the second leg, and there was a suspicion of the same as Napoli scored again two minutes into first stoppage-time.
Gokhan Inler's cross reached the far post and Cavani leant his shoulder into the ball to turn it home, the home fans letting off a firework in jubilation.
Villas-Boas refused to shut up shop after the interval and Marek Hamsik was forced to clear off his own line, while Florent Malouda drilled a volley too close to De Sanctis.
But Napoli should have punished another error when Meireles gave Cavani the chance to feed Lavezzi, who dragged wide.
Gary Cahill was booked for clattering into the livewire forward and Mata volleyed another shot straight at De Sanctis before a desperate Salvatore Aronica clearance denied Drogba a possible equaliser.
Napoli were not sitting back either and the latest Luiz howler saw them double their lead in the 65th minute, the defender kicking a long ball straight against Cavani, who squared past the stranded Cech for Lavezzi to steer into an unguarded net.
Villas-Boas responded by throwing on Lampard and Essien for Malouda and Meireles, with Lavezzi soon withdrawn for Blerim Dzemaili.
Branislav Ivanovic was unable to make the most of a goalline scramble and Napoli almost killed the match - and perhaps the tie - when Cole cleared Maggio's open-goal effort off the line.
Goran Pandev came on for Hamsik and he too might have made it 4-1 but Drogba also went close to giving Chelsea a tie-changing second away goal when he hooked wide.