Argentina were held to a 0-0 draw in Buenos Aires by Peru, leaving the two-time world champions outside the automatic qualification places as they head into the final round of fixtures next Tuesday.
It was another desperately disappointing display by Argentina, who once again struggled to turn a wealth of possession into goals.
Barcelona star Messi hit the post in the second half but could only watch in frustration after serving up a stream of chances for team-mates who failed to convert.
But with only two points separating third-placed Chile and seventh-placed Paraguay, the final standings could change dramatically depending on results on Tuesday.
The margin for error for Argentina, however, has narrowed after their latest setback, their third consecutive draw of a faltering qualification campaign.
Argentina's final qualifier is a challenging away trip to Ecuador in the thin air of Quito. Argentina have a poor record in the Ecuadoran capital, losing two out of three of their last World Cup qualifiers there and drawing the other. The Argentines' last World Cup qualifying win in Quito came in 2001.
- Uruguay on brink, Colombia crash -
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Brazil, who have already qualified in first place, were held to a 0-0 draw by eliminating Bolivia in La Paz earlier Thursday.
That left the focus on the teams jostling behind the five time champions for the three remaining automatic spots.
Uruguay, who are second with 28 points from 17 games, missed the chance to book their place in Russia after being frustrated 0-0 away at Venezuela.
The Uruguayans are all but assured of qualification however, needing only a draw or a win against lowly Bolivia in Montevideo next week to book their place.
South American champions Chile, meanwhile, resurrected their qualification hopes with a thrilling 2-1 win over Ecuador in Santiago.
Striker Eduardo Vargas drilled in a low shot on 22 minutes to put the 2015 & 2016 Copa America champions 1-0 up.
But Alex Ibarra equalised in the 82nd minute for Ecuador to silence the home crowd.
The win saw Chile climb from sixth to third in the standings. Chile will qualify automatically if they are able to beat Brazil in their final game next week.
In Barranquilla, Colombia threw away what looked to be a certain victory that would have put them within touching distance of qualification as they crashed to a 2-1 defeat to Paraguay.
Radamel Falcao scored with a deft lob to put Colombia 1-0 ahead in the 79th minute.
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.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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