Rafael Benitez's side beat Juventus 6-5 on penalties in Doha on Monday to end the year on a high note.
Napoli were twice behind in the match after goals from Carlos Tevez, but fellow Argentine Higuain also helped himself to a brace to ensure the match finished 2-2 after 120 minutes.
Higuain's second goal came with two minutes of extra-time remaining, before goalkeeper Rafael rose to the occasion in the shootout with saves from Giorgio Chiellini and Simone Padoin.
Former Real Madrid striker Higuain believes the Naples outfit proved they can be a force and has not given up hope of winning Serie A, despite Juventus being 12 points ahead of Benitez's men.
He told the club's official website: "We proved our value, I would like to dedicate this win to all our supporters.
"I'm extremely delighted, the team played a brilliant match, we proved that when there is more intensity and high pace we can fight against everybody.
"This cup cheers us and we will have a wonderful Christmas. We needed this huge satisfaction and we pulled it off with all our strength.
"There are still many months to go until the end of the season, we have all the qualities and we can reach the top. We strongly believe in our plan."
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