Led by Barcelona star Lionel Messi, the Argentines failed to convert a number of chances and now find themselves in sixth place in the South American qualifying group, level with Peru on 25 points but behind on goal difference.
The top four teams qualify automatically for Russia 2018, with the fifth-placed team facing a two-legged intercontinental playoff against New Zealand.
Brazil have already qualified as group winners, but behind them just four points separate second-placed Uruguay and seventh-placed Paraguay.
Argentina, who won the World Cup in 1978 and 1986, and who were beaten finalists at Brazil in 2014, will need victory against Ecuador in their final game on Tuesday to at least ensure a playoff spot.
Elsewhere in the group, Copa America champions and recent Confederations Cup finalists Chile eased their own qualification concerns with a 2-1 home victory over Ecuador, thanks to an 85th-minute Alexis Sanchez winner which came three minutes after Romario Ibarra had cancelled out Eduardo Vargas’ first-half opener for Chile.
The Chileans travel to Brazil for their final game, knowing that a draw should be enough to see them claim at least fifth spot. Second-placed Uruguay face Bolivia and know that their superior goal difference should see them secure an automatic place, whatever the result.
Fifth-placed Peru are at home to fourth-placed Colombia, and should Argentina fail to win, Messi and co. will be depending on the result of that game to decide their fate.
— #WCQ ⚽️🏆 (@FIFAWorldCup) October 6, 2017
Elsewhere on Thursday, reigning world champions Germany booked their place in Russia thanks to a 3-1 away win against Northern Ireland in European qualifying Group C.
England ensured automatic qualification as winner of Group F, after Harry Kane’s late goal gave them a barely-deserved win against Slovenia at Wembley.
#WorldCup line-up, so far:
— #WCQ ⚽️🏆 (@FIFAWorldCup) October 5, 2017