Midfielder Mejdi Traoui put the North Africans ahead just after half-time in hot and humid Omdurman, striker Zouhaier Dhaouiadi struck the second and substitute Oussama Darragi completed the scoring 10 minutes from full-time.
The teams drew 1-1 at the group stage 18 days ago, but this time there was no mistaking the superiority of the Tunisians against opponents who relied on a lone striker and rarely troubled goalkeeper and captain Aymen Mathlouthi.
Tunisia coach Sami Trabelsi dedicated the triumph to his countrymen who toppled dictator Zine el Abidine Ben Ali last month and forced him to flee his homeland for Saudi Arabia after 25 years in charge.
It was the first Pan-African success for the small country sandwiched between Algeria and crisis-torn Libya since they hosted and won the 2004 Africa Cup of Nations.
The Cup of Nations is open to all African footballers while the Nations Championship is restricted to those based at home. Among the teams Tunisia defeated en route to glory were title holders Democratic Republic of Congo.
Mudathir Eltaib scored his third goal of the championship eight minutes before half-time to give Sudan a 1-0 victory over Algeria in the third place play-off that preceded the final.
Mohamed al-Basha did the spadework by dribbling his way through the visitors defence before passing to Eltaib whose shot gave goalkeeper Cedric Si Mohammed no chance.
There were plenty of scoring opportunities in a lively second half but no goals and Sudan collected their first Pan-African tournament medals since staging and winning the 1970 Cup of Nations.