Rafael Benitez's side, who will face Fiorentina in the final, took the lead on the night and levelled the tie when Jose Callejon scored a close-range header from right back Christian Maggio's perfectly flighted cross after 33 minutes.
An attacking blitz from Napoli in the opening minutes of the second half saw Gonzalo Higuain double their lead from a corner and Jorginho net his first Napoli goal to seal their place in May's final.
Kevin Strootman compounded Roma manager Rudi Garcia's misery by being sent off in the 79th minute.
The Dutch midfielder was booked after a cynical foul on Callejon, before he received his marching orders immediately afterwards for sarcastically applauding referee Gianluca Rocchi.
Napoli will take on Fiorentina in the Italian capital after Vincenzo Montella's side came back from a 2-1 first leg defeat to Udinese to take the tie 3-2 on Tuesday.
(Reporting by Terry Daley; editing by Toby Davis) nL3N0LH64R
