Match ends, Congo 2, Burkina Faso 1.
Congo reached the quarter-finals of the Africa Cup of Nations for the first time since 1992 by topping Group A.
Congo needed a draw to progress and went ahead when Thierry Bifouma swept home Ferebory Dore's cross.
Burkina Faso required a win and offered little until the last 10 minutes when Aristide Bance scored at the far post.
Congo won it in the 87th minute when goalkeeper Germain Sanou punched the ball on to the shoulder of Fabrice Ondama and it trickled into the net.
Congo's qualification added to the remarkable record of manager Claude LeRoy, who has now achieved seven quarter-finals in eight appearances at the tournament with five different countries.
Congo had the best chance of a very disappointing first half in the 21st minute when Delvin N'Dinga played in Bifouma on the left-hand side of the penalty area, but the striker dragged the ball wide of the far post.
Burkina Faso, who reached the final of the last tournament in 2013, finally woke up as the match approached half-time.
First Jonathan Pitroipa set up Prejuce Nakoulma, who could not control the ball and Congo goalkeeper Christoffer Mafoumbi rushed out to clear.
Then Pitroipa received a pass inside the area, chested it down but sent his shot high over the bar.
The second half started in a much more eventful way with Dore heading a good chance past the near post from a 47th-minute corner.
Burkina Faso almost took the lead in remarkable fashion three minutes later.
Goalkeeper Sanou cleared the ball downfield from well inside his own penalty area and it reached the opposite area where it bounced over his counterpart Mafoumbi and rolled just past the post.
Bifouma put Congo in front a minute later from close range from a right-wing cross by Dore, who seemed to be clearly offside when he received the ball.
Burkina Faso needed to score twice to have a hope of going into the last eight but rarely looked likely to do that.
Congo nearly added to their lead with a 72nd-minute free-kick, but N'Dinga's powerful shot was saved by Sanou.
Burkina Faso finally found the net in the 81st minute when Mafoumbi spilled an Alain Traore free-kick, but substitute Issiaka Ouedraogo's finish was ruled out for offside.
Bance gave Burkina Faso's fans fleeting hope when he scored from Ouedraogo's cross, but 90 seconds later it was all over when the ball went in off Ondama as Congo secured victory.
Congo coach Claude LeRoy:
"It's incredible. I feel a lot of emotion and incredible happiness.
"We conceded a goal that shouldn't have stood because there was a foul on Bissiki at the start of the move, but although a 1-1 draw would have been enough, we hit back right away.
"We have come from nowhere. We knocked out Nigeria, the reigning champions, and now we have beaten Burkina Faso, who were runners-up last time. Anything that happens from now on is a bonus."
Burkina Faso coach Paul Put:
"The luck was not on our side."
- 12LitsingiSubstituted forGandzéat 89'minutes
- 5Bouka Moutou
- 10DoreSubstituted forOndamaat 75'minutes
- 13Bifouma KoulossaSubstituted forDouniamaat 63'minutes
- 9GouoSubstituted forBancéat 59'minutes
- 22NakoulmaSubstituted forTraoreat 58'minutes
- 21TraoreSubstituted forOuédraogoat 73'minutes
- Joseph Lamptey
- Shots on Target
Second Half ends, Congo 2, Burkina Faso 1.
Steeve Yago (Burkina Faso) wins a free kick in the defensive half.
Foul by Ladislas Douniama (Congo).
Corner, Congo. Conceded by Germain Sanou.
Attempt saved. Césaire Gandzé (Congo) right footed shot from outside the box is saved in the bottom left corner. Assisted by Fabrice N'Guessi.
Bertrand Traore (Burkina Faso) wins a free kick on the left wing.
Foul by Césaire Gandzé (Congo).
Substitution, Congo. Césaire Gandzé replaces Francis Litsingi.
Foul by Djakaridja Koné (Burkina Faso).
Delvin N'Dinga (Congo) wins a free kick in the defensive half.
Goal! Congo 2, Burkina Faso 1. Fabrice N'Guessi (Congo) with an attempt from the centre of the box to the centre of the goal following a set piece situation.
Foul by Mohamed Koffi (Burkina Faso).
Marvin Baudry (Congo) wins a free kick on the right wing.
Goal! Congo 1, Burkina Faso 1. Aristide Bancé (Burkina Faso) right footed shot from very close range to the bottom left corner. Assisted by Issiaka Ouédraogo with a cross.
Attempt missed. Fabrice N'Guessi (Congo) right footed shot from the right side of the box is high and wide to the right. Assisted by Marvin Baudry.
Foul by Charles Kaboré (Burkina Faso).
Prince Oniangué (Congo) wins a free kick in the defensive half.
Offside, Burkina Faso. Charles Kaboré tries a through ball, but Aristide Bancé is caught offside.
Corner, Burkina Faso. Conceded by Sagesse Babélé.