Nigeria’s win, their first at a World Cup finals since 1998, leaves them as favourites to join Argentina in the second round.
Argentina are on six points after beating Iran 1-0 earlier on Saturday to leave the Iranians on a point while the Nigerians are on four points.
Nigeria play Argentina in their final group game on Thursday — the Africans have lost all three times they have previously played the South American side in the group stages, losing 1-0 on the last occasion in 2010.
Nigeria were a completely different team to the one that had barely got out of a Sunday morning stroll in the 0-0 draw with Iran.
Emmanuel Emineke always looked a threat and it was he who created the goal, as he burst down the right and engaged in a race for the ball with veteran Bosnian skipper Emir Spahic, who tried vainly to obstruct the Nigerian.
However, the central defender had completely misjudged the situation as Emineke went the opposite side and outpaced him to collect the ball before unselfishly squaring it to Peter Odemwingie, with the Stoke City striker tucking the ball away.
Bosnia had little to offer, though they could claim that they had been robbed of a goal as Edin Dzeko put the ball past Vincent Enyeama, but it was wrongly ruled out for offside.
Dzeko, though, could have stolen a point at the death when he rose to meet a corner but his downward header was straight at Enyeama, who gratefully smothered it.
The Manchester City striker went even closer in time added on as his shot from inside the area beat Enyeama but cannoned back off the post.
The referee whistled for fulltime shortly after that with the Bosnians collapsing to the ground in despair and the Nigerians jumping for joy as they — after the Ghanaians drew with Germany earlier on Saturday — restored pride to the African challenge at the finals.
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