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Angel Di Maria and Lautaro Martinez netted first-half goals around Ben Brereton-Diaz's looping header as Albiceleste extended their unbeaten run to 27 games.
The victory improves second-placed Argentina's CONMEBOL World Cup qualifying campaign to 32 points from 14 games, while Chile is battling to reach Qatar 2022.
La Roja, who suffered their second straight home defeat, have 16 points from 15 games and are seventh in the standings, three points behind Uruguay in the fourth automatic qualification spot after it won 1-0 in Paraguay.
Paris Saint-Germain winger Di Maria silenced the home Calama crowd in the ninth minute when he curled home a trademark left-foot strike from outside the box for his 23rd international goal.
Blackburn Rovers attacker Brereton-Diaz leveled the game up in the 20th minute when he precisely headed over Argentina goalkeeper Emiliano Martinez from Marcelino Nunez's diagonal cross.
Argentina restored its lead, just as Chile goalkeeper Claudio Bravo had gestured to be substituted due to injury, with the veteran stopper unable to hold Rodrigo De Paul's long-range strike allowing Martinez to fire home the rebound in the 34th minute.
The visitor weathered Chile's late pressure, with Brereton-Diaz forcing a good low save from Martinez with an 84th-minute header.
