Ezequiel Lavezzi scored a brace and Edinson Cavani added the third after Juan Mata had given the visitors the lead.
Villas-Boas will now face more questions over his future with his side struggling in the league and hanging on in the FA Cup after a fifth round home draw with Championship side Birmingham City.
A 2-0 win at Stamford Bridge in the last 16 second leg in three weeks time would be enough for the Londoners to progress but on this evidence Chelsea don’t look capable of keeping a clean sheet against anyone.
The absence through injury of captain and star centre-back John Terry was marked as David Luiz and Gary Cahill were made to look vulnerable and incapable of plugging any defensive gaps.
And with Terry ruled out for the next six weeks as he needs a knee operation — news that was announced before the game — Chelsea’s defence doesn’t look likely to improve any time soon.
But that’s not to take anything away from Napoli who were scintillating on the counter attack — as they had been against Manchester City in the group stages.
Villas-Boas laughed in the face of his supposedly precarious position by picking a surprisingly attacking line up with Daniel Sturridge, Mata and Florent Malouda behind Didier Drogba.
It made for an entertaining game but Chelsea’s defence was too often exposed.
Gokhan Inler released Cavani after just nine minutes with Cahill’s slip giving the Uruguay forward time to control and shoot but Petr Cech came to his side’s rescue.
The Czech goalkeeper did so again when Lavezzi released the overlapping Maggio inside Luiz.
And yet it was largely against the run of play when Mata gave the visitors a 27th minute lead, helped in no small part by the pitch.
After a neat passing move Sturridge tried to slip the ball inside to the Spaniard.
Paolo Cannavaro was in the way but a bobble saw him slice his attempted clearance up in the air and Mata calmly let it drop and side-footed home from 10 yards.
The leveller came on 38 minutes as Lavezzi sold Raul Meireles a huge dummy, opening up space outside the box from where he curled a precise finish around Cech.
The third Napoli goal came on 65 minutes as Luiz hesitated under a long punt forward and Cavani nipped in front of him, drew Cech and slid the ball left for Lavezzi to roll the ball past Cahill on the line.