After a goalless opening period, the match at Nuevo Estadio de Malabo in Equatorial Guinea sprang to life in the second half, with Mateus opening the scoring for Angola before Alain Traore's excellent free-kick pulled the Stallions level.
But Angola, quarter-finalists in the last two editions of the continental showpiece, ensured themselves a winning start to the tournament when former Manchester United frontman Manucho found the net with a brilliant strike midway through the second half.
The win puts Angola top of Group B alongside Côte d'Ivoire, who defeated Sudan 1-0 earlier today. Angola shaded the early exchanges, with Geraldo Miguel's drive wide of the upright and a Sebastiao Gilberto free-kick threatening Daouda Diakite's goal.
Between those two openings, Burkina Faso carved out a chance when Paul Koulibaly saw his shot from the edge of the area blocked by Francisco Zuela.
Burkina Faso ended the half much the stronger side, with Traore volleying over in the 38th minute and Moumouni Dagano twice coming close to applying the finishing touch to good team moves.
Angola came out firing at the start of the second half and, two minutes in, almost went ahead when Andre Macanga flashed a dangerous shot across the face of the goal.
Goals at either end
Sixty seconds later Lito Vidigal's men were ahead. Stallions defender Bakary Kone was guilty of not clearing effectively, and when the ball fell to Mateus the striker showed good composure to cut inside and fire home a powerful low shot.
Burkina Faso were rocked by the goal but regrouped to level after 56 minutes. Jonathan Pitroipa drew a foul on the edge of the area after some good approach play, and from the resulting free-kick Traore stepped up to bend the ball around the wall and into the net.
But Angola were pegged back for just 11 minutes before Manucho intervened, his fine effort from outside the area leaving Diakite grasping at thin air and securing his team a perfect start to their campaign.