All the goals were scored before 25 minutes were played.
First Felipe Gutierrez put Chile ahead with a header from a corner-kick in the 10th minute but Angel Di Maria equalised in the 19th minute with a crisp strike from the left side of the penalty area.
Gabriel Mercado got a second for Argentina five minutes later, latching onto a silky Lionel Messi flick to volley home the eventual winner.
The game was tightly contested in the second half and four bookings were forthcoming for Argentina, who managed to hold on for the win.
Argentina are fourth out of 10 teams in Conmebol qualifying for Russia 2018, sitting on eight points after five matches. Early leaders Ecuador have 13 points.
Chile and Brazil both have seven points, but Selecao have a game in hand against Uruguay tomorrow morning.
Peru and Venezuela drew 2-2 in the day's other game.
There are 18 rounds in South American World Cup qualifying, with teams playing each other home and away. The top four finishers qualify and fifth place goes to a play-off.