The Copa America champions join Brazil as the second South American team to qualify for the tournament.
Their place was confirmed after Chile’s 2-0 defeat at home by Ecuador later on Tuesday, together with Uruguay’s 3-0 loss in Bolivia earlier on.
Argentina are now unbeaten in 27 matches over the past two years.
Paris St-Germain striker Lionel Messi, playing his first game since late October because of injury, drew a decent save from Liverpool keeper Alisson in the final moments in San Juan.
Brazil came closest to scoring when Manchester United midfielder Fred hit the top of the bar in the second half.
The two sides’ World Cup qualifier in Sao Paulo in September was abandoned after just five minutes because Brazilian health officials objected to the participation of three Argentine players they believe broke quarantine rules.
Argentina coach Lionel Scaloni said qualification capped a “magnificent” year for his side, who beat Brazil in Rio de Janeiro to win the Copa America in July.
“Winning the Copa, qualifying for the World Cup unbeaten – it was a dream,” he added.
“Having qualified so far in advance, in a really difficult qualifying section, is something we should be proud of.”
Leaders Brazil and Argentina are the only two unbeaten teams in South American qualification.
There are two automatic spots remaining, with third-placed Ecuador looking in a strong position to qualify, six points clear of Colombia and Peru, with four matches to play.
The race for the final automatic spot is set to be tense, with six sides separated by just four points and only bottom-placed Venezuela realistically out of the running.
Colombia drew 0-0 with Paraguay on Tuesday, while Peru beat Venezuela 2-1 to move into fifth place and the inter-confederation play-off spot.
The next two rounds of fixtures take place in January and February next year.