Last week's 0-0 draw in south Wales was succeeded by a more exciting affair in Naples but the result went against the Swans who were agonisingly close to drawing level at the death to go through on away goals.
Nevertheless, Rafael Benitez's Partenopei got the job done over Garry Monk's Swans to move through to the Round of 16 thanks to goals from Lorenzo Insigne, Gonzalo Higuain and Gokhan Inler while Jonathan de Guzman was on target for the visitors.
The opening goal came in the 17th minute when Higuain played a neat ball for Insigne who managed to deftly lob over Swans keeper Michel Vorm.
Napoli keeper Reina was on hand to come up with a crucial save with minutes remaining, managing to tip over Dwight Tiendalli's point blank header from a free-kick, which essentially got the Italian club through.
As Swansea chased an equaliser - which would have had them progress by virtue of the away goal rule - Napoli pounced with Inler advancing towards goal and slotting home to give his side a flattering two-goal triumph.
Benitez's side will now prepare for the Round of 16 where they will meet Portuguese giants FC Porto on March 13 in the first leg and March 20 in the second.
2013/14 UEFA Europa League - Round of 32 second leg
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