Argentina now sit in 5th place in the CONMEBOL standings, the playoff spot for next summer's showpiece.
Messi played Alejandro Gomez in on goal in the 57th minute, but Pedro Gallese made an excellent save of his close range shot from an angle. The fans were there, in full voice throughout - but the situation on the pitch was depressingly familiar as Lionel Messi and his charges limped to another draw that could have catastrophic consequences.
Argentina were the runner-up to Germany in the World Cup three years ago in Brazil, will play on Tuesday against Ecuador in the thin air of Quito in the Andes.
Peru, who are in the fifth and final qualification place, will host Colombia in Lima.
Messi isn't the only global household name which could miss out on Russian Federation 2018.
In the night's other game, second-placed Uruguay were held 0-0 in Venezuela.
La Albiceleste face a daunting task at home against a roaring Peru side, who are one place above the home team with a superior goal difference.
Messi had already retired from the national side before reconsidering in a bid to try and lift an elusive World Cup.
"I see them being very capable of winning a World Cup next year", he continued.
Chile's match-winner Alexis Sanchez.
Colombia missed out on the opportunity to seal their place at next year's finals after they were beaten 2-1 at home by Paraguay, who kept alive their slim hopes of making it to Russian Federation. Thirty-two goals in 80 games mark him as the Incas' all-time top scorer, a title he claimed from Cubillas in the 2016 Copa America, and with five strikes so far in this qualifying campaign, he is tied with the impressive Edison Flores as his nation's best marksman.
The goal was the red-hot Falcao's 14th in his last 13 matches for club and country.
Oscar Cardozo bundled in the equaliser for Paraguay in the 89th minute and then Tony Sanabria punished poor goalkeeping by David Ospina to poke in a second in injury time to clinch the win.
Syrian players celebrate during the 2018 FIFA World Cup Asian Qualifier Group A Final Round match against China in June.
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