The team's tactical rigidity was rewarded as they drew level four minutes later when, after a goalmouth scramble, the ball fell to Alfred Finnbogason who side-footed home past a grounded Willy Caballero in the Argentina goal. The game then looked like it was heading towards a stalemate until Iceland conceded a penalty with half an hour remaining on the clock.
This could well be the last World Cup for Messi and like his Real Madrid and Portuguese rival, Ronaldo, he will be aiming to to make his mark - although he will do well to match Ronaldo's performance against Spain yesterday.
"It will be unfair to give some player the role of marking Messi" he said.
Ian Wright was shell-shocked...
"Messi misses a penalty and somehow, somewhere, I think Ronaldo may be winking", tweeted former Barcelona and England forward Gary Lineker.
The World Cup rookies from the tournament's smallest nation are suddenly legitimate contenders for the knockout stage. "It's a very even World Cup and you're seeing that, because all the games are very close", he added. "So yes we have trained that, we have worked to improve that to see if we can limit that capacity".
His fellow superstar Messi, with whom he has monopolised the world player of the year award for a decade, is under huge pressure to secure his first major global trophy and make amends for Argentina's painful loss to Germany in the 2014 final.
Messi's missed penalty was Argentina's only clear-cut chance in the second half, although Cristian Pavon's bouncing cross drew a fine late save from Halldorsson. Iceland were able to shut him out, and by doing so, cut off Argentina's main avenue in attack.
Iceland plays in Group D with Lionel Messi's Argentina.
Indeed, they had some decent chances to win the match too.
After that we'll know if Peru can match up to their fantastic support in Russian Federation when they face Denmark at 5pm.
"We don't think it's a miracle, it's great to work from the FA and especially the players, no team can win games without good players".
"People say we celebrate when we won a point - wait and see how we celebrate when we've won a game", said Iceland coach Heimir Hallgrimsson.