Tuesday's game was as good as done after six minutes, by which time Argentina had already opened up a two-goal lead. Two more goals early in the second half merely confirmed Argentina's superiority.
In the night's other game, Bolivia defeated the United States 1-0 on a first-half goal by Marco Etcheverry. The teams are now tied at three points.
Bolivia concludes the first round against Chile on Friday, while the Americans face Argentina.
Chilean fans had expected the worst following their team's 2-1 defeat by the United States on Saturday but even the most pessimistic would have been surprised at the team's dreadful start.
After just 20 seconds, Ariel Ortega slipped a pass between two Chilean defenders, leaving Batistuta with only goalkeeper Marcelo Ramirez to beat. The Fiorentina striker calmly placed his shot into the far corner.
Five minutes later, midfielder Diego Simeone scored with an angled shot which went in off Ramirez's foot.
Argentina relaxed for the rest of the first half but the threat from Batitusta was ever-present and he missed a good chance in the 26th minute when he found himself with a free header but put his effort wide.
The Argentines also found time for some rough play and Juan Jose Borrelli was lucky to receive only a yellow card for a shocking tackle on Rodrigo Perez.
Argentina made another explosive start to the second half.
In the 52nd minute, Batistuta scored his second goal after being set up by a clever backheel by Ortega.
Three minutes later, Batitusta had a chance for a hat-trick when he broke clear on the right, but instead of shooting, he selflessly laid the ball off for Abel Balbo to score the fourth.
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