With Diego Maradona watching on from the stands, Messi failed to convert from the spot in the second half of an eventful Group D opener at the Otkrytie Arena in Moscow.
Sergio Aguero had fired the beaten finalists from four years ago ahead in the 19th minute, finally breaking his World Cup duck at the ninth attempt with a rising left-footed drive.
Yet debutants Iceland refused to melt on the main stage, Alfred Finnbogason capitalising on Willy Caballero's weak punch to score his country's maiden goal in the history of the tournament just four minutes later.