Serbian Branislav Ivanovic smashed home the winning goal in the 105th minute of an enthralling clash to keep the English flag flying in the competition after both Manchester clubs and Arsenal had fallen by the wayside.
Trailing 3-1 from the first leg, it was Chelsea's much-criticised 30 somethings who provided the inspiration having struggled domestically under recently sacked coach Andre Villas-Boas.
Didier Drogba opened the scoring and captain John Terry's header made it 2-0 just after the interval only for Napoli to regain the advantage through Gokhan Inler's low drive.
Frank Lampard's penalty 15 minutes from time made it 4-4 on aggregate to send the tie into extra time and it was the 34-year-old Drogba who again showed his class, providing the perfect cut back for Ivanovic to send Chelsea through.
"He finished it unbelievably, like a striker really," Lampard told ITV.
"It was a symbol of the team's spirit, the way he finished that. A performance like that could change our season. We're just happy to be in the hat. If we play with that ability tonight we can take on anyone."
Interim coach Roberto Di Matteo jumped for joy on the bench as Chelsea kept their dream of a first Champions League triumph alive and ended Napoli's hopes of reaching the last eight for the first time. Only AC Milan from Italy now remain.
"This could top them all for sure," said Terry, whose side lie fifth in the Premier League. "We showed what Chelsea are made of tonight."
The match started amid a feverish atmosphere and Chelsea went close to an early breakthrough when the ball dropped to Daniel Sturridge and his first-time shot produced a scrambling save by Morgan De Sanctis at his near post.
Apart from that though the opening 25 minutes belonged to the visitors, who clearly had not arrived at Stamford Bridge purely to protect their two-goal advantage.
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They should have gone in front when danger-man Edinson Cavani slid in at the far post to meet a low cross from Christian Maggio but the Uruguayan could only find the side-netting.
Chelsea had looked cumbersome with Drogba a frustrated figure upfront but the Ivorian showed why he has been such a feared predator over the years in the Champions League when he put his side ahead after 28 minutes.
Ramires cut in from the left flank and curled a menacing cross into the area that was met by the sweetest of headers from Drogba to give De Sanctis no chance.
Michael Essien then sent a shot narrowly wide as Chelsea ended the half on top.
Chelsea began the second half as they had ended the first and within three minutes Terry combined with fellow old warrior Lampard to make it 2-0, arcing a textbook header beyond De Sanctis from the midfielder's corner.
The emphasis was now on Napoli to score and they did not take long to respond.
When Terry's headed clearance went out to Swiss midfielder Inler, he chested the ball down and rifled a shot past Cech from 25 metres to spark scenes of delirium from the 2,500 Napoli fans behind the goal.
With 15 minutes to go Chelsea were gifted their third goal when substitute Andrea Dossena needlessly handled and Chelsea's trusty penalty taker Lampard made no mistake from the spot to make it 4-4 on aggregate.
Extra time was wide open before Ivanovic sealed the tie with glee.
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