It was a thoroughly deserved third African crown for Nigeria, who dominated the game throughout and could have had several more goals were it not for some sloppy finishing.
But Mba's splendid goal - which involved a magnificent bit of ball juggling - proved enough for them, though Burkina Faso leave South Africa with their heads held high after a wonderful run to the final.
The night belonged to Nigeria, however, with manager Stephen Keshi becoming the first man to win the tournament as both player and coach.
The two sides had met in their opening match of the tournament, with Burkina Faso grabbing a draw in injury time that ultimately saw them top the group - and Nigeria started as if they meant to make amends for that surprise stalemate.
Efe Ambrose almost opened the scoring after just eight minutes as his powerful header from Victor Moses's free kick went just inches over.
Two minutes later Ideye Aide Brown was on hand to poke goalwards after a shocking mistake by Burkina Faso goalkeeper Daouda Diakité, who spilled the ball to his opponent as he charged out at a corner - but Ideye failed to find the target.
That seemed likely to be the story of the opening half: Nigeria enjoying the lion's share of possession and chances but not making a breakthrough.
The feeling that fate might be against them was only enhanced five minutes before half time when Moses's brilliant work drawing in three defenders ended as his shot ricocheted back towards him.
The opportunity seemed over, even as the ball bounced out to Mba - but what the midfielder did next was worthy of winning any final.
His first touch popped the ball up into the air and guided it away from two defenders; his second touch was a sublime volley poking the ball into the far corner, leaving Diakite rooted to the spot.
The incredible strike, reminiscent of Paul Gascoigne's famous goal against Scotland at Euro '96, would prove to be the only one of the match. Nigeria continued to control the game in the second half, so much so that they enjoyed the luxury of spurning several excellent chances.
Moses was culpable as he took too much time while one-on-one against Diakite on the hour mark, and unbelievably Ahmed Musa fell flat on his face after tripping on the admittedly poor playing surface with 17 minutes left when Moses had delivered him a gilt-edged chance.
Those blunders would have been rued if Nigeria keeper Victor Enyeama had not produced a brilliant save to palm Wilfried Sanou's drive around the post, but in the end Mba's earlier strike proved decisive - and it would be hard to imagine a finer goal to decide a final anywhere in the world.