Emmanuel Emenike shot Nigeria in front in the first-half, as the Super Eagles looked in dominant control.
But they failed to kill the game off despite creating a multitude of chances. And when Efe Ambrose was sent off with 15 minutes to play, things took a dire turn.
Keshi threw on Kenneth Omeruo to steady his backline, and the Eagles looked like they would hold on for the point, but a rash decision to go for the killer goal late on left the Nigerian exposed, and Burkina Faso broke with extreme menace.
The Nigeria defence failed to clear the ball and the substitute, Traore arrived late to poke home from close-range, and break Nigeria hearts.
The result leaves Group C all square, after Zambia and Ethiopia also drew 1-1 earlier on in the day.