Lionel Messi scored a superb hat-trick as Argentina came from behind to win away in Ecuador and qualify for the 2018 World Cup in Russia.
Argentina began the day in sixth position and in danger of not qualifying for a World Cup for the first time since 1970.
They made a terrible start in the high-altitude location of Quito when the hosts went ahead after 38 seconds through Romario Ibarra's goal - the quickest goal Argentina had ever conceded in a World Cup qualifier.
However, Argentina, runners-up in Brazil in 2014, fought back with Messi - just when he was needed most - in stunning form.
The five-time world player of the year equalised after 12 minutes when he linked up with ex-Manchester United midfielder Angel di Maria and stabbed home.
His second goal came eight minutes later with a powerful strike from the edge of the area before a fine solo goal in the second half sealed the victory and with it Argentina's passage to Russia next summer.
Brazil had already qualified and Luis Suarez scored twice as Uruguay beat Bolivia 4-2 to qualify, with Colombia also advancing with a 1-1 draw in Peru.
Peru finished fifth in South American qualifying and will now meet New Zealand in a two-legged play-off.
Arsenal's Alexis Sanchez and Chile are out after losing 3-0 in Brazil.