The Zambians' third straight stalemate left them emulating Algeria, who failed to reach the quarter-finals as reigning champions in 1992.
Zambia missed out after Nigeria nabbed the runners-up spot in Group C, courtesy of their 2-0 win over Ethiopia in the match being played simultaneously in Rustenburg. That left the Nigerians level on five points with Burkina Faso, but in second on goal difference. As surprise winners of the mini-league, the Burkinabe's reward is a quarter-final clash with the Group D runners-up, either Togo or Tunisia.
Collins Mbesuma joined Southampton's Emmanuel Mayuka in the Zambia attack, the Orlando Pirates forward replacing captain Christopher Katongo, with talismanic goalkeeper Kennedy Mweene taking over the skipper's armband. Coach Herve Renard made one more change, bringing in Hichani Himonde for veteran defender Joseph Musonda.
Burkina's captain Moumouni Dagano was on the bench for the second time, with Benjamin Balima taking the Qatari-based striker's place. Daouda Diakite was between the Burkinabe posts with first-choice keeper Abdoulaye Soulama suspended for his red card in the Ethiopia rout, and Florent Rouamba came in for Aristide Bance.
Alain Traore's deadly left foot, already the author of three goals for Burkina Faso, tested Mweene with a well struck 30-metre free-kick in the opening seconds. That unhapppily was to be his last impact on the game as in the eighth minute he was stretchered off with an untimely left thigh injury. Bance stepped in to replace the stricken Lorient player.
Renard was forced into an unscripted change himself, with Musonda in for the injured Davies Nkausu.
Playing in their orange 'away' strip, Zambia had a great chance to open the scoring in the 17th minute when a defensive blunder by Mady Panandetiguiri let in Mbesuma, but his shot went straight into the grateful hands of Diakite.
After the restart, Renard made a tactical switch, bringing on attack-minded Mulenga Mukaka for Isaac Chansa.
Approaching the hour, Mbesuma's header off a corner went flying over the crossbar as Zambia began to put the Burkinabe backline under pressure.