Aguero, wearing the number 10 shirt in absence of injured captain Lionel Messi, could have registered a hat-trick but blasted the ball over the bar in the 75th minute after goalkeeper Asmir Begovic had parried a shot from his strike partner Rodrigo Palacio.
Argentina, who played out a goalless draw with Ecuador in New Jersey on Friday, ended their US tour unbeaten as coach Alejandro Sabella tried two experimental line-ups and tested defensive variations.
The Bosnians, whose appearance in the 2014 World Cup finals in Brazil will be their first, might have taken an early lead but shots from strikers Vedad Ibisevic and Edin Dzeko went narrowly wide of Sergio Romero's posts.
Argentina, though, enjoyed more possession with busy midfielder Angel Di Maria creating a string of chances.
Di Maria's headed pass into the box led to the first goal with Begovic fouling Palacio as he went for the ball and Aguero following through to steer it into the net between two defenders five minutes before half-time.
"It was important to finish the year well playing like this and that we didn't concede goals in either match," Aguero told broadcasters TyC Sports.
The striker, lucky the referee missed his kick in retaliation for a dangerous challenge in the 56th minute, found the net 10 minutes later with a left-footed volley from the left after a fine pass from deep in midfield by Maxi Rodriguez.
Substitute Erik Lamela, on for Di Maria, had two good chances in the dying minutes while Dzeko, kept in check for most of the match, had a stinging shot beaten away by Romero.