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Bosnia may have been forgiven for thinking that they were in for a long night, but instead the newcomers looked to fight back and started to pose problems for the two-time former world champions.
Argentina tried to increase the tempo just after the half-hour mark and Javier Mascherano's effort from distance needed to be punched clear by Begovic.
However, the Bosnians continued to push for an equaliser and Manchester City forward Edin Dzeko came close to scoring after working himself into space, but he couldn't keep his effort down.
Four minutes before the interval, the best chance for the World Cup debutants came when Senad Lulic headed a corner goalwards, but Romero was on hand to keep out the Lazio midfielder.