Nigeria proved too strong in the deciding match for the workman-like Burkinabe, who were out-muscled and out-sprinted at Soccer City and never looked like repeating the heroics that got them to the final.
Mba's goal came from a botched clearance that fell perfectly for him but he conjured up a piece of brilliance by flicking the ball over the head of defender Bakary Kone and then slamming it into the net with goalkeeper Daouda Diakite rooted to his line.
It was one of just a few clear chances on the night, most of them for Nigeria who looked a class above their game but outgunned opponents.
Dual honourNigeria, whose coach Stephen Keshi became the second man to win the Nations Cup as both coach and player, might well have added two or three more too the score with a little extra care in front of goal.
Brown Ideye had chances just after halftime and again with eight minutes to go but overran the ball and Ahmed Musa slipped at a crucial moment when he was put in the clear by Victor Moses.
Moses was also guilty of squandering opportunities on the counter attack as Burkina Faso were kept pegged back in their own half.