Goals from Angel Di Maria and Ever Banega secured a deserved three points for Argentina, who exacted sweet revenge for their defeat to the Chileans in last year's Copa America final.
Chile substitute Jose Fuenzalida scored an injury time consolation for the holders. The Argentines will now be firm favorites to progress to the quarter-finals as Group D winners with games against Panama and Bolivia to come.
Injured Argentina captain Messi watched from the substitutes' bench at Levi's Stadium after failing to recover in time from a sore back suffered in a friendly win over Honduras last month.
That missed chance set the tone for the early exchanges of an entertaining first half which saw Argentina create the lion's share of opportunities without managing to find a breakthrough goal.
Manchester United defender Marcos Rojo was the next to test Chile goalkeeper Claudio Bravo, unleashing a dipping shot from 20 yards which the Barcelona stopper comfortably saved in the 17th minute.
In midfield meanwhile a fascinating battle for supremacy was unfolding between Argentina's rugged enforcer Javier Mascherano and Chile's combative Bayern Munich star Arturo Vidal.
Chile, fielding the core of their victorious Copa America side, gradually grew into the game. But it was Argentina who continued to look the more threatening and they might have taken the lead on 22 minutes after a lightning fast counter-attack.
Di Maria and Banega combined delightfully down the left flank before the ball was transferred to Napoli's Gonzalo Higuain whose attempt on goal was deflected wide for a corner.
Sanchez drew a save from Romero in a bright Chilean start to the second half but it was Argentina who opened the scoring on 51 minutes. A swift counter-attack saw Banega release Di Maria, whose quick low shot flew past Bravo and into the bottom corner as the Chile goalkeeper struggled to get his body into position.
The game continued to have an edge with Di Maria and Gary Medel both receiving yellow cards for an off-the-ball scuffle shortly afterwards.
In injury time Fuenzalida grabbed a late consolation with a headed goal from a free-kick but it was too little too late.
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