Sunday Mbah fired the Super Eagles ahead with a superb volley five minutes before the break after a period of pressure saw Burkina Faso, competing in their first final, succumb to Stephen Keshi's side.
Wilfried Sanou came close to levelling for the Stallions midway through the second half but his brief flash of brilliance was extinguished by a top-drawer save by Vincent Enyeama.
Nigeria were hot favourites ahead of the match against the minnows from west Africa due to their 12-game unbeaten record.
Their win means coach Keshi becomes only the second man to win the cup as coach and player, following in the footsteps of Egyptian Mahmoud Al Gohari.
Efe Ambrose had the first chance of the match when he headed over the bar from Victor Moses' free-kick in the seventh minute before Burkina Faso goalkeeper Daouda Diakite came off his line to take a ball above his own defender's head, only to fluff his take, with Brown Ideye's resulting weak shot looping over the bar.
Nigeria kept up the pressure, Aristide Bance wasting a good chance when his low, drilled 25-yard free-kick flashed just wide of Enyeama's right post.
Burkina Faso were struggling to get out of their own half and Nigeria's dominance told five minutes before the break, when Mbah volleyed past Diakite from the middle of the box. After some good build-up play, Moses' shot was blocked and looped up to Mbah, who plucked the ball from the air to fire the Super Eagles to a deserved lead.
After the break, Moses wasted a golden chance to score on the counter-attack when he failed to pull the trigger when one-on-one with Madi Panandetiguiri.
The Nigeria defence were then called upon to keep out two testing corners before Super Eagles goalkeeper Enyeama denied Sanou's powerful strike with a fantastic diving save to tip it around the post.
However, Burkina Faso remained unable to find that elusive cutting edge, with substitute Moumouni Dagano firing over the bar with his stoppage time free-kick in their last meaningful attack.