The vital goal was scored by Osaze Odemwingie in the first-half.
The game started in frantic fashion from the blast of the referees whistle as both sides tested each other for size.
The first notable chance of the game fell to Nigeria after Emmanuel Emenike won a free-kick which was taken by Ahmed Musa in the 3rd minute. The Bosnian defence cleared Musa's effort, but it fell to Ogenyi Onazi who sent his effort over the bar.
Musa won a free-kick on the edge of the Bosnian box after he was pulled down by Hajrovic in the 7th minute. But the resulting free-kick by Odemwingie went inches wide off the right post.
Nigeria continued to press forward with the likes of Musa, Mikel Obi and Emenike in the thick of things. Onazi tested Begovic with a shot from distance after receiving a pass from Babatunde in the 15th minute.
Musa tried to surprise the Bosnian keeper with a shot from the right wing after receiving the ball from Odemwingie in the 20th minute, but Begovic was up to the task.
Edin Dzeko scored for Bosnia a minute later, but his goal was cancelled for offside.
Dzeko forced Enyeama to make a great save four minutes later after Onazi missed his tackle and allowed the strike break forward.
The Bosnians were gifted a number of chances courtesy of careless play by Nigeria's midfielders, with Onazi and Mikel the biggest culprits.
Odemwingie gave Nigeria the much needed goal in the 29th minute after Emenike broke in powerfully from the right to square the ball for Odemwingie slotted the ball past Begovic.
After the goal, Nigeria sought to slow down the pace of the game, but it didn't stop Dzeko from forcing a close save from Enyeama in the 33rd minute.
Bosnia had a number of half chances, but Nigeria managed to carry their lead into the break.
Dzeko wasted a chance to equalize for Bosnia in the 48th minute, as he ballooned a cross from Hajrovic. On the other end, Babatunde forced a fine save from Begovic with a shot from 20 yards.
Emenike continued to lead Nigeria's onslaught in the game as he muscled his way continually into the vital area of the opponents, but there were no further goals in the game.
There were however scary moments in the dying minutes as Bosnia almost grabbed an equalizer, as Dzeko's effort came off the post in added time. But Nigeria held on to secure their first World Cup win in 16 years.