Two years after reaching the quarterfinals at the European Championship, Iceland earned its first point in its first World Cup match, holding two-time champion Argentina to a surprising 1-1 draw.
Messi endured a tough afternoon, squandering the chance to win it with a missed penalty in the second half to continue his miserable record from the spot.
Aguero fired Argentina ahead in the 19th minute, finishing brilliantly on the turn from 12 metres, but they kept the lead for only four minutes before Finnbogason swept home a loose ball to equalise. Argentina pressed for the victor in the second half, but in the end had to settle for a point.
Two minutes later, Argentina took the lead in stunning fashion.
Messi stepped up but Iceland goalkeeper Hannes Halldorsson made the save to deny the Argentinian icon his first goal of the tournament. Croatia and Nigeria are also in the group.
"Iceland could go out and play the best game of our lives and still lose against a fantastic team like Argentina", he said.
While Hallgrimsson got his approach spot on, the same can not be said for his Argentina counterpart Jorge Sampaoli, whose pre-match assertion that everything would be centred around Lionel Messi seemed to upset the balance of his side.
"Beyond the goal scored against us, I don't think our transitions were fast enough and we should have hurt our opponent more". "They were defending, their only chances to score were from a set piece or looking for the second play".
"I had a good feeling it would go this way today", he said of his dive to his right to stop Messi's uninspired effort.
However, against the run of play in the 23rd minute, Iceland pushed forward through Birkir Bjarnason and Aron Gunnarsson.
As expected, it was the South Americans who dominated the opening exchanges as they moved the ball around, while Iceland were tight and compact at the back.
Iceland's performance belied their underdog status, relying more on organization at the back to disrupt Argentina's potent forward line that also includes Angel Di Maria of PSG and Gonzalo Higuain of Juventus.
Despite their success in France, though, manager Heimir Hallgrimsson has called this "the biggest game in the history of Icelandic football". "There are some things you hope or wish for, and saving a penalty from Messi in the first game is definitely one of them", Halldorsson said.