Mateus and Manucho scored in the second half for the Angolans, helped by sloppy play from their opponents, with Alain Traore scoring a superb equaliser in between.
Burkina were badly let down by their defence as their forwards created more than enough chances to win the game. Angola joined Ivory Coast on three points after the Elephants beat Sudan 1-0 earlier on Sunday.
The first half, while far from a classic, produced half- chances for both sides with Angola looking slightly more dangerous.
The game burst into life three minutes after the break when a sequence of mistakes in the Burkina area ended with Hamadou Tall losing possession to Mateus who cut inside and fired a left-foot shot past Daouda Diakite.
Burkina conjured up a superb equaliser 10 minutes later when French-based midfielder Alain Traore curled a 25-metre free-kick around the wall and left Carlos Fernandes stranded.
The goal brought the Stallions to life and they looked capable of winning the match until the defence lost possession again.
This time, Manucho benefited and the Real Valladolid player fired a left-foot shot past the stunned Diakite from outside the area.
Burkina were far from finished and Beli Moumouni Dagano should have equalised when he was allowed a free header from close range but his effort went straight to a grateful Carlos Fernandes.
Dagano was denied again by the goalkeeper as Angola, who resorted to blatant time-wasting, were forced to defend desperately
