Michael Emmanuel Papo gave Nigeria, who also won the African championship in 2001 and 2007, the crucial ticket with his 77th-minute goal, with the Burkinabes unable to respond until the final whistle.
Fatai Amoo’s team started the competition on a shaky note losing by the odd goal to Cote d’Ivoire, and played a 1-1 draw with Ghana in their second game in the three-team Group B.
They looked to be on their way home until Cote d’Ivoire trashed Ghana 3-1 to allow the Eaglets get into the last four.
Nigeria’s opponents in Wednesday’s final will be the winner of Friday’s second semi final clash between Cote d’Ivoire and Niger Republic.
The venue for the final match will be Togo’s main stadium, the Stade Kegue.