''We're going to the quarters! We're going to the quarters!'' the Ivory Coast players sang in their changing room.
Salomon Kalou opened the scoring in the 16th minute and Bakary Kone headed in an own goal in the 82nd to hand victory to the pre-tournament favorite despite another unconvincing performance from its English Premier League-based stars.
Earlier, Sudan twice rallied from defensive errors to draw 2-2 with Angola in the other Group B match at Nuevo Estadio de Malabo.
The results mean Angola and Sudan retained hopes of progressing, but Burkina Faso was eliminated with a match to go.
''It was an incredible injustice that we lost this match,'' said Burkina Faso coach Paulo Duarte, who refused to talk about his future. ''Burkina Faso played a great match, had a great attitude, but they scored two goals. Football is like that. What more can I say?''
The final group matches will be on Monday when it's Sudan vs. Burkina Faso and Ivory Coast vs. Angola.
''I'm satisfied with the spirit of the group, though it's true that there are a lot of things to improve,'' Ivory Coast coach Francois Zahoui said.
Didier Zokora returned to the Ivory Coast starting lineup after serving a suspension and was the only change from the 1-0 win against Sudan, with Igor Lolo dropping to the bench.
Duarte made three alterations to the team that lost 2-1 against Angola, including forward Prejuce Nakoulma to provide more support for Moumouni Dagano in attack.
Ivory Coast took the lead when Kalou pounced on a low cross that brushed off Yaya Toure, and hit a left-foot shot past Daouda Diakite in the Burkina Faso goal.
Despite a front line of captain Didier Drogba, Kalou and Gervinho, Ivory Coast looked disjointed in attack and Yaya Toure struggled to impose himself on the game from an advanced midfield position.
Gervinho looked to be in a particularly wasteful mood after he skipped away down the left flank but sent his attempted pass straight into the arms of Diakite.
Drogba collected the ball in the middle of the pitch just before halftime and struck a dipping shot that Diakite fumbled, but Gervinho was penalized for the follow-up.
''It was a big game between two big teams,'' Duarte said. ''If there was going to be a winner in the first half, then I think it would have been Burkina Faso. We played fantastic football.''
At least the attraction of watching Ivory Coast's England-based players swelled the crowd, with empty seats much less noticeable for the west African derby than the earlier match between Sudan and Angola.
After the break Ivory Coast was again struggling for control against a neighbor rated more than 50 places beneath them.
Kalou pulled up with an apparent muscle strain and was replaced by Max Gradel with 25 minutes to go.
''I hope he will recover soon because he is a very important player for us,'' Zahoui said.
Dagano headed against the top of the crossbar in the 72nd, but Ivory Coast avoided a nervy finish when Kone headed a deep free kick over his own goalkeeper in the final stages.
''It's very important to get through the next round. Our objective is to finish in first place in the group,'' Zahoui said.