The African nation struck via Peter Odemwingie in the 29th minute in Cuiaba, and held firm in the second half as Bosnia failed to create a goal that would have kept their maiden finals campaign alive.
Odemwingie slotted past Stoke City team-mate Asmir Begovic at the Arena Pantanal, although Bosnia were unfortunate not to have led eight minutes earlier when an Edin Dzeko goal was incorrectly ruled out for offside.
Nigeria produced plenty of chances on goal and deserved to open the scoring, with Odemwingie's free-kick in the seventh minute deflecting narrowly wide of the upright, while Ogenyi Onazi - who tried his luck from range on a few occasions - forced a low save out of Begovic on 14 minutes.
For all their instability at the back, Bosnia settled into the game and should have been credited with the game's opening goal when Dzeko got in behind and found the back of the net in the 21st minute - only for the assistant's flag to be incorrectly raised.
Dzeko was clearly Bosnia's best chance of scoring the opener, and minutes later he unleashed a shot from inside the area that Nigeria goalkeeper Vincent Enyeama was forced to produce a strong save to deny the Manchester City man.
The Bosnians would be further aggrieved with the officials, when they felt they were denied a foul in the lead up to Nigeria's opener - with Spahic left on the ground, as Emmanuel Emenike squared a ball for goalscorer Odemwingie.
It was almost déjà vu for Spahic in the 60th minute, as Emenike brushed aside the Bosnian skipper, but he had cover this time around.
