Christian Eriksen stunned the hosts with a goal direct from the corner flag within three minutes, but Dries Mertens equalised with an historic goal, making him the all-time club top scorer.
The 1-1 result was enough for Napoli to qualify 2-1 on aggregate, setting up a Final against Juventus on Wednesday June 17.
“We are facing a Juventus side that are accustomed to winning, have the mentality of great champions, so we can fight it out and have our say. We know that it’ll take a great performance to bring home the trophy.”
Lorenzo Insigne dedicated the result to Gattuso, who lost his sister to a terminal illness earlier this month.
“I want to thank the whole football world, as everyone was very close to me and my family” the coach told RAI Sport.