Playing without superstar striker Lionel Messi, Argentina dominated the tempo most of the match against the Bosnians, who like the Albiceleste, have already booked their place at the 2014 FIFA World Cup Brazil™.
In-form Aguero opened the scoring on 40 minutes after Stoke City goalkeeper Asmir Begovic was unable to snuff out the danger which ensued after a cross from Napoli's Federico Fernandez.
Aguero doubled his tally on 66 minutes, rifling a left-footed shot past Begovic following a swift break in the area.
It was another lethal exhibition of goalscoring from Aguero, who has scored 13 times in all competitions for Premier League side City this season.
Argentina, with only one loss in 12 matches, were coming off a goal-less draw with Ecuador three nights earlier.
That lone defeat came at the hands of Uruguay in a qualifier after a World Cup berth had already been secured.
A pro-Bosnian crowd cheered on the Dragons, with the St. Louis area boasting the largest collection of Bosnians outside their homeland.
The match was played in the home stadium of Major League Baseball's St. Louis Cardinals, who lost to the Boston Red Sox in last month's World Series.