It was a result that took winning coach Stephen Keshi into the record books as he equalled the feat of late Egyptian Mahmoud El Gohary by winning gold medals as a player and a coach.
Among the rewards for the Super Eagles was a $1.5 million first prize and a place at the FIFA Confederations Cup in Brazil, where they will face world and European champions Spain, Tahiti and Uruguay.
Nigeria were forced into a late pre-match change when striker and four-goal leading scorer Emmanuel Emenike was ruled out by a hamstring injury sustained in the semi-final rout of Mali and experienced Ikechukwu Uche took his place.
Burkina Faso were able to retain the team that started against Ghana in a semi-final settled by a shoot-out after the red card given to midfielder Jonathan Pitroipa was rescinded when the referee admitted he erred.
It was only the third time the countries have met in the 56-year competition with Nigeria beating then-Upper Volta 4-2 in 1978 and Burkina Faso snatching a stoppage-time 1-1 draw in a Nelspruit group game last month.
The Mba goal gave the Super Eagles a deserved 1-0 half-time lead after 45 minutes that followed a predictable script with Nigeria dominating possession and scoring chances while the Burkinabe relied largely on counter-attacks.
Mba, one of two home-based stars in the starting line-up, struck on 40 minutes with a penalty-box flick over Mohamed Koffi and a left-foot shot into the far corner past helpless goalkeeper Daouda Diakite.
It was an opportunist goal by Mba and his second of the tournament, having struck a superb match-winner in the 2-1 quarter-final defeat of pre-tournament title favourites Ivory Coast.
Nigeria should have taken the lead much earlier as Diakite spilled a cross on 10 minutes into the path of Brown Ideye, whose shot at an unguarded goal was just too high.
A combination of Nigerian midfield creativity and a couple of defensive howlers by the Burkinabe offered several half chances to the Super Eagles that were squandered.
The early second-half exchanges mirrored the first period with the Nigerians pressing for a second goal that would leave opponents fielding a lone striker in Aristide Bance with a mountain to scale.
Diakiate did well to push away a hard, low Ideye cross-cum-shot and Moses should have done better in a two-on-one situation that favoured the Eagles only to timidly surrender possession with the Burkinabe goal in sight.
Although Spain-based Uche was a goal-scoring star of the qualifying campaign, he was making no impact on the final and gave way to Ahmed Musa nine minutes after half-time.
There was another Nigerian substitution not long after — this time enfored — with full-back Elderson Echiejile limping off to be replaced by Juwon Oshaniwa, while the Burkinabe introduced Wilfried Sanou for Florent Rouamba.
As the game moved into the final quarter there were chances at both ends with unmarked Musa slipping as he was poised to shoot inside the box and a Sanou drive at the other end finishing just wide of the far post.