And Hannes Halldorsson joined Finnbogason in the country's footballing folklore by thwarting Messi from the penalty spot in the second half to preserve a memorable point.
By the second half, Messi pushed further forward, presumably with the aim of getting him in more risky areas, but if anything, that made Argentina more predictable.
The problem for Iceland is that once you take care of Messi, you still have Gonzalo Higuain, Sergio Aguero, Angel Di Maria and the rest to worry about.
But Iceland's Finnbogason fired home from close range just minutes later after Argentina failed to clear a cross.
Israeli Defense Minister Avigdor Liberman suggested Saturday that soccer soccer star Lionel Messi missed a crucial World Cup penalty because of Argentina's last minute withdrawal from a warm up game with Israel.
The South Americans are outright favourites to dominate the group along with probably Croatia, notwithstanding the dangers of Nigeria.More news: Sarah Sanders calls Trump's salute to North Korean general 'common courtesy'
Nonetheless, it was Iceland who had the game's first good chance, Birkir Bjarnason missing the target from a good position after Willy Cavallero and Marcos Rojo combined to give the ball away from an Argentina goal kick.
That's a rough start to the tournament for Argentina, and especially rough for Messi given the missed opportunities and timing of it all.
However, undeterred by the setback of conceding first, Heimir Hallgrimsson's side hit back.
Despite his success with Barcelona, Messi still has not won a major honour with Argentina.
This will be the first ever encounter between Argentina and Iceland.
The throw-in from Hordur Magnusson was nearly used to devastating effect just before the break, with Sigurdsson pouncing on indecision only to see his snapshot pushed away. Argentina suffered a heart-breaking loss in the final to Germany in extra time at World Cup 2014 in Brazil, and they'll be focused on getting back to the final this tournament.
The World Cup in Russian Federation might likely be the last opportunity for Lionel Messi to lead his national team to the silverware and delete the lone remaining criticism of his legacy. "It was an uncomfortable match, because Iceland was playing very defensively, blocking all the possible spaces, but we did everything we could for Argentina to win".