Messi won a free kick in the fifth of five minutes of stoppage time, and his bid to join rival Cristiano Ronaldo as a last-minute hero went into the wall.
Hannes Halldorsson used to make zombie films for a living but it was watching videos that let Iceland's goalkeeper outwit Lionel Messi and save a penalty on Saturday that gave his side a shock World Cup point.
But those in Messi's camp have an out following Argentina's 1-1 draw with Iceland: The tiny Nordic nation did the same thing to Ronaldo two years ago at the Euros. The ref pointed to the spot and naturally Messi was decided amongst his teammates he was the worthy choice to play "God".
But the Barcelona ace's lackluster record on penalties continued, as he stepped up and fired a weak shot at the flawless height and velocity to gift Iceland keeper Hannes Halldorsson an easy save.
Without him they were beaten 6-1 in a friendly against Spain in March and they have only played once since, beating Haiti 4-0, with Messi scoring another treble.
Messi tried his luck from outside the area soon afterwards, his curling strike held by Halldorsson - but, out of the blue, Iceland were level after 23 minutes, Alfreo Finnbogason stabbing home amid defensive chaos.
If, 18 hours apart, Messi and Ronaldo produced chalk-and-cheese performances, exactly two years and two days apart, Iceland came up with two of the most determined defensive displays you are ever likely to witness at the worldwide arena.
Nine minutes from the end, Messi curled a superb strike narrowly wide from the edge of the D, and Argentina threw Gonzalo Higuain into the fray as they pressed for a late victor. "It was the advantage", he said.
Argentina did play with some urgency getting to the end of the game but it was too little, too late.
For now, the Icelanders will savour what they richly deserved. And what ended as a draw felt more like a victory for Iceland - and there is just more than one reason why everyone is cheering for the new football team. "We know how we can win football matches, and against a team like Argentina, that it's just a fact they have superior individuals with superior skills playing better teams in better leagues than the Iceland players".
Argentina seemed to have its breakthrough in the second half when Aguero went down after a collision and earned a penalty. Messi stepped up to take the resulting penalty but nothing came of it. But they were massively outnumbered in the 45,000-capacity stadium by Argentina fans, and Iceland coach Heimir Hallgrimsson did not understand why. 'All they did was defend and attack with nothing but long throw-ins. Croatia and Nigeria are bound to pose challenges of their own.
With a population of 335,000, the European nation will have to stop one man Lionel Messi who has not had a good love affair with the World Cup in his three previous tournaments.