Salomon Kalou's first-half strike and a bizarre own goal from Bakary Kone were enough to give the Ivorians their second straight win in Group B and a place in the last eight with a match to spare.
Burkina, who again paid for defensive mistakes as they did in their 2-1 defeat by Angola, were eliminated.
However, Ivory Coast's performance is unlikely to appease critics angry with coach Francois Zahoui's safety-first tactics with a team boasting six English Premier League players in the starting line-up.
The Elephants produced a similarly dreary display in their opening 1-0 win over Sudan, another theoretically much weaker team.
"I am satisfied, there are things to improve and our target is to go as far as possible," said Zahoui. "We didn't concede goals for the second game in a row and that is another plus."
"They were very, very determined, they played with passion and caused us a lot of problems."
Burkina coach Paulo Duarte said: "We played a perfect game, only a team which has a lot of qualify can play the way we did today."
The game could have taken a different turn if Burkina Faso had been awarded a penalty in the ninth minute when Jonathan Pitroipa was tripped in the area, but play was waved on.
Instead, the Elephants went ahead in the 16th minute when Kalou scored with a full-blooded volley after two Burkina defenders failed to clear Didier Drogba's cross.
The Ivorians sat back, allowing Burkina to get into the game as Alain Traore had three long-range efforts on goal before the break.
Pitroipa set up Burkina's best chance after half-time when he tricked his way to the byline and Traore's side-footed effort was stopped by a grateful Boubacar Barry.
Gervinho missed two good chances on the break for the Ivorians, who often pulled eight players back into their own half even when in possession, before Kone's misfortune.
Arthur Boka sent a long free-kick into the Burkina area and Kone, unmarked, sent a backwards header looping over the stranded Daouda Diakite.
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