Lionel Messi and Gonzalo Higuain struck within minutes of each other half an hour into the match, taking their personal tallies to seven, with Chile pulling one back through substitute Felipe Gutierrez in added time at the end of the game.
Argentina have 20 points from nine matches, three more than Ecuador, who drew 1-1 away at Venezuela, and four ahead of Colombia, who have a game in hand.
They rode their luck in the opening half hour when Chile created several chances, then showed superior finishing to settle the match.
"We have forwards of huge standing who normally never forgive [mistakes]. Argentina were sharper with their finishing," Argentina coach Alejandro Sabella told reporters.
"We knew Chile would take the ball from us a lot and we had to be very concentrated in defence."
Travelling is a risky business in the tight nine-nation South American group, so Argentina have taken out good insurance with Tuesday's win because anything can happen in the remaining seven rounds of matches next year.
Uruguay, the top South American team at the 2010 finals in South Africa where they finished fourth, lost 4-1 to Bolivia in La Paz, where striker Carlos Saucedo bagged a hat-trick.
The Uruguayans, renowned for their strong defence, have conceded 11 goals in their last three away matches and taken one point out of a possible 12, yet are in fifth place.
Fifth is good enough for a play-off, just like three years ago when they needed to beat Costa Rica over two legs to pick up the last berth for South Africa.
"We still have chances [of qualifying]. If Bolivia, who had five points, thought about going to the World Cup and will continue thinking that with this victory, why can't we with 12 points?" said coach Oscar Tabarez.
"We made mistakes that make us think we're not well, but we also did things that make us realise we're not bad," he told reporters after his team struggled in the thin air of La Paz.
VENEZUELA FOURTH
Fourth-placed Venezuela, looking to reach the finals for the first time, and bottom team Paraguay, are separated by a mere five points. That underlines how little it takes for a side to appear to have slipped in or out of contention.
Venezuela returned to action after a bye on Friday and were held to a 1-1 draw by Ecuador in Puerto La Cruz but the point was enough to enter the top four, who qualify directly for the 2014 finals in Brazil.
Playmaker Juan Arango gave Venezuela an early lead with a magnificent shot from outside the box but similar stunning efforts from the home captain were saved and one hit the bar.
Ecuador, who have a perfect home record of five wins but have picked up only two points in their four away matches so far, equalised through Segundo Castillo in the 24th minute.
Paraguay, having lost three matches under new coach Gerardo Pelusso, beat Peru 1-0 in Asuncion with a headed goal from central defender Pablo Aguilar to regain their hopes of reaching their fifth finals in a row.
