Napoli were twice behind in the match on Monday after goals from Carlos Tevez but Benitez's own Argentine frontman – Gonzalo Higuain - ensured the match finished 2-2 after 120 minutes.
Higuain's second came with two minutes of extra-time remaining, before goalkeeper Rafael produced heroics in the shootout with saves from Giorgio Chiellini and Simone Padoin.
After the latter had missed from 12 yards the Napoli boss hailed the achievement as one of the best of his career.
"It's one of the best games of my life, as to win against a side like Juventus is remarkable," the Spaniard told Rai Sport.
"We dedicate this to all the Napoli fans who were with us today and watching from home.
"Rafael was excellent, Higuain made the difference in attack, but the whole team did well, everyone deserves this title."
The victory sees Napoli win the competition for only the second time, the first coming in 1990 when they were captained by Diego Maradona.