Lionel Messi hit the post for Argentina in the first half but the World Cup winners had their goalkeeper Emiliano Martinez to thank for keeping them on level terms before Lautaro's late strike settled a pulsating clash in front of 82,000 fans at MetLife Stadium in New Jersey.
There were enough openings for the 15-times Copa America champions to get the breakthrough much earlier but a combination of poor finishing and an inspired performance from Chile's 41-year-old goalkeeper Claudio Bravo left the score deadlocked.
The home of the NFL's New York Jets and New York Giants -- and venue for the 2026 World Cup final -- was transformed into a home venue for Argentina and the expectant crowd saw Messi and company dictate proceedings in the early stages.
Messi's strike partner Julian Alvarez forced Bravo into a save in the 22nd minute with a first-time shot after Nicolas Gonzalez had pulled the ball back from the byline.
Chile were doing a good job of neutralising Messi, closing him down with three players on occasions.
But the eight-times Ballon d'Or winner was inches away from an opener in the 36th minute with a shot from 25 yards which clipped the outside of the post.
Chile had twice left Argentina distraught with victories in the Copa America finals of 2015 and 2016, the latter at MetLife Stadium on a night when Messi reacted by briefly quitting the national side.
But while Chile proved stubborn, there is a real swagger about the world champions and a belief that they can always turn a game their way.
As Argentina piled on the pressure, Bravo did well after the break to parry out a blast at the near post from Nahuel Molina and then showed great reactions to push a fierce Nicolas Gonzalez drive against the bar.
Chile threatened on the counter and twice Argentina goalkeeper Martinez had to be at his best to deny drives from Rodrigo Echeverria.
The decisive moment came when Chile failed to clear an in-swinging corner from Messi and Lautaro Martinez pounced to grab the winner, confirmed after a lengthy VAR offside check.
Lautaro should have added a second after a breakaway from Angel Di Maria but in the end the solitary goal was enough to make it two wins out of two for the World Cup winners and book their place in the next round with a game to spare.
"I got in there and I was able to score. These games are always like that, we have to keep playing in the same way treating the games in this way, as they are all going to be complicated," Lautaro told TyC Sports.
Canada triumph
In other Copa America action, Jonathan David scored the only goal as Canada reignited their campaign with a 1-0 victory over 10-man Peru in sweltering Kansas City.
Lille striker David -– who is reportedly being targeted by Manchester United and Chelsea -– once again demonstrated his eye for goal with a cool finish to secure all three points at Children's Mercy Park Stadium.
A game played in scorching afternoon sunshine -– with on-pitch temperatures nudging towards 100 degrees Fahrenheit (38 degrees Celsius) -– saw one of the two referee's assistants collapse with apparent heat exhaustion just before half-time.
Canada, beaten 2-0 by Argentina in the opening game of the tournament, took the lead in the second half after Peru had been reduced to 10 men following the dismissal of Miguel Araujo for a wild foul on substitute Jacob Shaffelburg that sparked a melee amongst players from both teams.
Referee Mario Escobar initially only gave Araujo a yellow card for his ugly studs-up challenge but the punishment was upgraded after a VAR review.
That dismissal tipped a close game in favour of Canada and the breakthrough finally came on 74 minutes with David's goal from a sweeping counter-attack.
Left-winger Shaffelburg played a sensational first-time cross-field pass to David, who took one touch without breaking stride and then buried a right-foot finish into the bottom corner past goalkeeper Pedro Gallese.
Peru pressed forward in search of an equalizer, but Canada goalkeeper Maxime Crepeau denied Christian Cueva with a fine one-handed reflex save from a volley before keeping out Paolo Guerrero's injury-time free-kick.
