The Argentina skipper has now missed four of the last seven penalties that he has taken for club and country combined.
Substitute Cristian Pavon almost scored the victor for Argentina four minutes from time but his curling effort was saved by Halldorsson.
Although in the second half it seemed Lionel Messi's side would make tables turn, thanks to epic save by Hannes Halldorsson, even though Argentina earned a penalty, Messi could not turn it into Buenos Aires' glory.
Coach Heimir Hallgrimsson led a light training session allowing opportunities to Iceland's unused substitutes to stretch their legs, while the likes of Gunnarsson and goalkeeper Hannes Halldorsson, who saved a second-half penalty from Messi, jogged gently around the pitch. The Iceland goalkeeper dived to his right and got two hands behind the ball.
Argetina found little inspiration as they came up against two organised, defensive Icelandic banks happy to sit in deep. That gives us all a few days to replace the blown-out speakers on our laptops.
Argentina went on to stamp their authority on the game, dominating time on the ball and eventually going ahead thanks to Sergio Aguero, who struck home his first World Cup goal with a classy pirouette inside his penalty area.
Despite Argentina's dominance, Iceland held on valiantly to not concede. - Alfred Finnbogason's goal was Iceland's first shot on target in the competition.
Argentina came into the contest looking for vengeance for their 2014 World Cup Final heartbreak, with five players from that starting eleven selected for this clash, including star man Lionel Messi.
The ball belonged to Argentina for the majority of the first half but it wasn't like Iceland expected anything different. "I had a good feeling that he would go this way today".
Birkir Bjarnason missed a gilt-edged chance when he side-footed wide after nine minutes, and it came as no surprise when Iceland equalised. It was Aguero's alertness, seizing on a mishit Marcos Rojo shot, pivoting and lashing a shot past Halldorsson, that brought the first goal.
"We are bluntly honest about our ability - we know how we can win games". Football fans can live stream all World Cup games in English or Español on fuboTV (Try for FREE).
As the end approached, Halldorsson capped a man-of-the-match display with a smart stop from a Cristian Pavon cross that was headed for the far corner.
While the result was not on the scale of that Iceland produced to eliminate England from Euro 2016, it was a major boost for the tiny nation, who retain hopes of advancing from a group that also includes Nigeria and Croatia.
There were brief moments of quality but Iceland's resilience limited Messi to long range efforts, never getting close enough to inflict the damage we all know he can.
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