Paris Saint-Germain star Di Maria -- reeling from the death of his grandmother only hours earlier -- scored one goal and set up another as the two-time world champions avenged their defeat to Chile in last year's Copa America final.
Di Maria opened the scoring on 51 minutes and emotionally held a T-shirt up to the sky emblazoned with the message: "Grandma, I will miss you so much."
Moments later Di Maria then set up Argentina's second for Ever Banega, to complete a man-of-the-match performance.
Argentina coach Gerardo Martino revealed afterwards Di Maria had kept his loss a secret from him.
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"I just learned that five minutes ago that his grandmother died," Martino said. "He didn't tell me anything, he was feeling well to play."
Di Maria's virtuoso display secured a deserved three points for Argentina, who will now fancy their chances of topping Group D 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.
But the Barcelona superstar's absence was barely noticeable, with Nicolas Gaitan slotting into Argentina's attack and making an instant impression, hitting the woodwork with a header after only two minutes.
Argentina dominated the early exchanges before Chile, fielding the core of their victorious Copa America side, gradually grew into the game.
Chile came closest to breaking the first half deadlock in the 30th minute, when Alexis Sanchez burst onto a layoff from Arturo Vidal to go in on goal.
Sanchez drew another save from Romero in a bright Chilean start to the second half but it was Argentina who opened the scoring six minutes after the break.
Eight minutes later it was 2-0, Di Maria turning creator this time with a deft pass to Banega whose low shot took a slight deflection off Mauricio Isla to deceive Bravo.
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.
Chile's Argentina-born coach Juan Antonio Pizzi bemoaned mistakes which cost his team goals.
Twice Chile ceded possession cheaply in midfield, leading to Argentina's two goals.
"The mistakes were crucial," Pizzi said. "They cost us two goals."
It was Chile's third straight defeat -- but Pizzi was bullish about his team's chances of coming back.
"We believe we're going to get into the next round," he said. "I know we have difficult games ahead of us, but we're going to continue working hard and we have belief to move to the next round.