Di Maria netted a long-range goal to open the scoring with Chile leveling via Ben Brereton-Diaz.
But Lautaro Gonzalez scored the winner in the 34th minute after Claudio Bravo could not hold Rodrigo De Paul’s drive.
Argentina’s win extended their unbeaten run to 27 games, dating back to July 2019. It also came without Scaloni in the dugout after testing positive to COVID-19 while Messi remained in Europe after his recent diagnosis.
Today we were without the best in the world and our coach as well but we got the victory and this is also for them, Di Maria told reporters.
Argentina have already secured qualification for the 2022 World Cup but continue to impress with their ability to get results, having lifted last year’s Copa America.
“Everything is always much easier when Leo is here,” Di Maria said.
“The important thing is that we keep working like weve been doing and bringing joy to Argentines.”
Elsewhere, Brazil had a stoppage-time reprieve after conceding a late penalty which was overturned by the VAR in a 1-1 draw away to third-placed Ecuador.
Brazil’s Liverpool goalkeeper Alisson was sent off twice during the game but both decisions were rescinded by the VAR in a chaotic game where both teams were reduced to 10 men.
Uruguay won 1-0 at Paraguay with Luis Suarez netting the winner to end their four-game losing run in qualifying and move them back up to fourth.