A late header from captain Sagesse Babele was all the hosts needed to book their place at the last four of the competition. Earlier, Junior Makiesse saw his first half opener cancelled by Burkina Faso defender Ziem Somda in the second half.
An improved second half performance kept the Burkinabes on the path of at least a point from the game only for a defensive lapse in the closing stages to deny them in the balanced encounter.
The Congolese went up after five minutes through Makiesse, with a shot that deflected off Burkina Faso defender Emmanuel Gora before going past goalkeeper Kouakou Koffi.
‘Les Etalons’ came back strongly and Somda restored parity with a spectacular free-kick that caught Congo goalie Christoffer Mafoumbi off guard on 62 minutes.
With both sides guilty of spurning chances, the hosts left it late with Babele heading home from a Julsy Kaya corner kick three minutes from time.
Elsewhere in Brazzaville, Hamza Farag scored on the stroke of time to power Sudan to victory at the expense of Zimbabwe.
On Sunday, Congo will face Zimbabwe whilst Sudan and Burkina Faso battles it out in the other fixture.