The 25-year-old started the match for the world champions alongside Rodrigo De Paul and Chelsea's Enzo Fernandez in the engine room for the hosts.
Mac Allister enjoyed a stellar first section of the match, opening the scoring for Argentina in the 48th minute, beating Gabriel Arias in the Chilean net.
Strikes in the final 10 minutes of the contest from Atletico Madrid new man Julian Alvarez and Roma's Paulo Dybala sealed a comfortable victory for La Albiceleste.
After seven games of qualifying, Lionel Scaloni's troops sit top of the CONMEBOL section, 12 points ahead of seventh-placed Bolivia who as it stands are heading for an intercontinental playoff.
Liverpool's Mac Allister suffers injury blow
Despite a positive evening in terms of the result for Argentina, there was considerable concern for the fitness of Mac Allister at the end of the game.
The 25-year-old was forced off in the 79th minute of the match due to a muscle issue, with the midfielder replaced by Manchester United winger Alejandro Garnacho.
Argentina boss Scaloni was unable to provide a definite answer when asked whether Mac Allister would be fit for his side's clash with Colombia on Tuesday.
As a result, the Liverpool man has to be considered as a doubt for Arne Slot's side ahead of the return of club football at the end of next week.
Should Mac Allister have stayed in England?
Following the first few days on the Argentina camp, Scaloni revealed that Mac Allister had missed team training due to physical discomfort.
At this point, the midfielder was a doubt to feature for the World Cup winners against Chile, although the Liverpool man went on to start the match.
In hindsight, that decision to use Mac Allister on Thursday night might not have been the smartest from Scaloni, with the ramifications of that choice potentially impacting Arne Slot's side this month.