Published: 2021-06-15 05:12:53 BdST
Messi curled a superb free kick into the corner of Claudio Bravo's net from 25 metres after 33 minutes.
Chile equalised 13 minutes into the second half when Vargas followed up to head home the rebound after Arturo Vidal's penalty was tipped on to the bar by Emiliano Martinez.
The result extended Argentina's unbeaten run to 14 games under coach Lionel Scaloni, a sequence dating back to the 2019 Copa America semi-final.
Paraguay take on Bolivia in the second Group A game later on Monday, with Uruguay, the fifth team in the section, debuting on Friday.