The Lorient forward’s late intervention cancelled out Emmanuel Emenike’s first-half strike as Nigeria ended with 10 men after Celtic’s Efe Ambrose saw red.
The first chance of the game fell to Nigeria in the 13th minute but Brown Ideye’s first time shot from Ahmed Musa’s wicked right-wing cross cleared the crossbar.
However, the two-time winners took the lead 10 minutes later as Emenike finished past Abdoulaye Soulama after a deft flick from strike partner Ideye.
Ideye continued to threaten throughout the opening period although Musa’s tame 39th minute effort was as close as Stephen Keshi’s side came to a second.
Burkina Faso, winless in 17 Africa Cup of Nations matches prior to this fixture, looked to exploit the counter-attack but failed to register any meaningful attempts at goal in the first-half.
Ten minutes after the restart, Paul Put’s side were indebted to Soulama who was quick off his line to prevent Musa latching onto Chelsea midfielder Jon Obi Mikel’s clever through-ball.
Burkina Faso were creeping back into the game and in the 63rd minute, veteran striker Moumouni Dagano’s right-footed shot across goal was touched behind by Vincent Enyeama.
Two minutes later, Nigeria should have put their West African neighbours to bed as substitute Ikechukwa Uche slashed wildly over when well placed in the box.
Burkina Faso’s spirits were lifted in the 74th minute as Ambrose saw red for a second yellow card for a foul on the lively Jonathan Pitroipa.
As the game entered the final ten minutes, Villarreal forward Uche again blazed high and wide after cutting in from the right flank but blazed high and wide.
Traore had the final say as he coolly side-footed past Enyeama from Pitroipa’s cut back to secure Burkina Faso’s first point in the competition since 1998.
Both teams now have the opportunity to take a stranglehold on Group C with Nigeria facing holders Zambia and Burkina Faso playing Ethiopia.