The Burkinabe went 3-0 up through Steve Yago's poked finish, Andre Onana's own goal and Djibril Ouattara's header.
But roared on by the home supporters, Cameroon hit back via Stephane Bahoken and skipper Vincent Aboubakar, who netted twice in the last five minutes.
No extra time meant the match went to penalties with Blati Toure missing.
It was a disappointing end for Burkina Faso, who looked in total control after 49 minutes, but five-time winners Cameroon responded in superb fashion before converting all five of their spot-kicks.
