Second-half goals from Alexis Mac Allister, Julian Alvarez and Paulo Dybala sealed all three points in front of the sold-out home crowd.
Argentina are top of the South American qualifying standings on 18 points, five clear of second-placed Uruguay, who play Paraguay on Friday.
The Copa America champions were without captain Lionel Messi, who sustained an ankle injury during the final in July and will also miss their next qualifier against Colombia on Tuesday.
There was also a tribute to Angel di Maria at the Monumental stadium, following the winger’s retirement from international football.
Liverpool midfielder Mac Allister opened the scoring three minutes after half-time from an Alvarez cross, before the Atletico Madrid forward doubled Argentina’s lead with a long-range effort.
Substitute Dybala added a third goal in stoppage time with an assist from Manchester United winger Alejandro Garnacho.