Napoli needed two late goals from Gonzalo Higuain and Gokhan Inler to beat Swansea 3-1 and reach the final 16 of UEFA Europa League on Thursday.
Napoli, who held Swansea 0-0 in the first leg, went ahead in the 17th minute when Insigne latched onto Higuain's headed flick and lobbed a deft finish over the advancing Michel Vorm.
Swansea responded strongly to equalise 13 minutes later, and looked comfortably on their to a final-16 place, until 12 minutes from time when Higuain's goal smashed their hopes.
An unfortunate ricochet off Ben Davies fell kindly for Higuain, who smashed the ball beyond a helpless Vorm.
Inler rubbed salt into the wound in the final minute of stoppage time, coolly slotting beyond Vorm as Swansea left themselves exposed in chasing a second equaliser.
Napoli head coach Rafa Benitez said he knew Swansea would make troubles for his side.
"I was convinced Swansea would cause us problems. I expected a difficult game, but we remained tight and didn't get too stretched out, so we looked for and found the spaces to win the match," he said.
He suggested that there was psychological difference between Swansea and Napoli.
"Swansea had nothing to lose and came to Naples without pressure, whereas it was a different situation for us," he said.
In the round of 16, Napoli will meet Porto, a side which left Benitez impressed by their skill.
"They will always be a strong side and their League is packed with Brazilians, so there's a lot of technical quality," Benitez said.
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