The City striker played a pivotal role as his nation breezed past Bolivia 3-0 in La Paz.
First-half goals from Enzo Fernandez and Nicolas Tagliafico put Lionel Scaloni’s side in control before an 84th minute Nico Gonzalez strike ensured they went beyond the challenge of the hosts.
Argentina were without Lionel Messi, who Alvarez partnered with such success in last year’s World Cup, but that mattered little on the night.
The result leaves Argentina on six points from their first two games in the continent-wide group of 10.
In the October international break, they will host Paraguay before heading to Peru.
Alvarez will now return to Manchester to prepare for City’s Premier League trip to West Ham United on Saturday 16 September.