Rafa Benitez's side grabbed the lead on aggregate in the 78th minute, when Christian Maggio's cross from the right hit first Chico Flores, and then Ben Davies, allowing Argentine Gonzalo Higuain to sweep home somewhat fortuitously past Swansea goalkeeper Michel Vorm.
As the Welsh side desperately sought the second goal that would send them through, Napoli broke on the counter-attack, and Gokhan Inler was afforded time and space to net the third and complete the Serie A side's 3-1 aggregate victory.
Napoli now face Porto in the last 16, after the Portuguese champions beat German side Eintracht Frankfurt on the away goals rule.
10’ - SWANSEA THREATEN: Hernandez plays an incisive pass down the right channel, and Emnes' cultured chip is cleared off the line by Albiol. What a counter-attack from Swansea.
16’ - NAPOLI TAKE LEAD: Williams, Tiendalli and Flores start the inquest, as Insigne breaks through the offside trap to run onto a Higuain header and chip the ball deftly over Vorm to make it Napoli 1-0 Swansea.
20’ - CHANCE FOR A SECOND: Williams is dragged out to mark Insigne, leaving Higuain free in the centre, but the Argentinian shoots wide again when well-placed.
30’ - VISITORS DRAW LEVEL: Swansea have scored the away goal! De Guzman pulls off Bony down the left-hand side of the box and makes it 1-1 on the night, and 1-1 on aggregate. Credit to Routledge as well for bringing Albiol out wide with his run.
40’ - REINA STOP: Henrique does a comedy slip as Bony runs at him down the left of the area, but the Ivorian shoots straight at Reina.
61’ - SWANSEA PENALTY APPEAL: Tiendalli thinks he should have had a penalty, after he is tripped by Ghoulam in the area. It was probably minimal contact though.
67’ - NAPOLI BACK ON THE ATTACK: Inler finds Insigne on the left of the area, but Flores is alert to block the Napoli winger’s shot after Tiendalli misses the first challenge.
68’ - SWANSEA COUNTER: Swansea counter quickly, and Hernandez floats a lovely ball into the box for Bony. The Ivorian has run the length of the pitch, but his powerful header is straight at Reina.
79’ - HIGUAIN STRIKES: Higuain makes it Napoli 2-1 Swansea. Maggio's cross is intercepted by Flores, and the ball ricochets off Watson, allowing the Argentinian striker to sweep home past Vorm.
87’ - REINA TO THE RESCUE: Napoli are panicking here, and Ghoulam fouls Dyer again down the right. Reina does superbly to tip Tiendalli's firm header over the bar from Hernandez's free-kick.
89’ - NAPOLI DEFENDING FRANTICALLY: Napoli clear Tiendalli's shot. Watson then superbly blocks Higuain as Napoli break two-on-one on the counter.
90’ - INLER SEALS IT FOR NAPOLI: Hamsik breaks down the right, and Higuain finds Inler to net past Vorm to make it 3-1.
Swansea have now played 43 matches this season - two more than any other team in the Premier League.
Jonathan De Guzman's goal was Swansea's first in the Europa League for 381 minutes.
MAN OF THE MATCH
Wilfried Bony, Swansea - The Ivorian is always a handful for defenders physically, and Henrique struggled against the 24-year-old in the Stadio San Paolo. However, there was an added guile to Bony’s game in Naples, with the highlight a superb pass into the channel in the 34th to set up a Wayne Routledge chance.
Napoli: Reina 7, Maggio 7, Henrique 6, Albiol 6, Ghoulam 6; Inler 7, Behrami 7; Insigne 7, Pandev 6, Callejon 7; Higuain 7. Subs: Britos 6, Hamsik 7, Mertens 7.
Swansea: Vorm 7, Tiendalli 7, Williams 7, Chico 7, B Davies 7; Canas 7, De Guzman 7; Routledge 6, Emnes 6, Pablo Hernandez 6; Bony 8. Subs: Taylor 6, Pozuelo 6, Dyer 7.