Last summer's beaten World Cup finalists came into the contest with less of a stellar cast than usual due to last night's Champions League final.
It was one-way traffic from there as Aguero fired Gerardo Martino's side further ahead from the penalty spot within four minutes, before tapping home from point-blank range moments later.
Aguero latched onto Javier Pastore's cushioned header to drill home his third on 51 minutes, while Di Maria added a fifth from the penalty spot shortly after.
A spate of second-half substitutions appeared to stifle Argentina's fluency, and Gonzalo Higuain - who replaced Aguero - missed a fine chance for a sixth in the final quarter.
Argentina, who were paired with Uruguay, Jamaica and Paraguay in Group B, kick off their Copa America tournament against the latter in La Serena, Chile, next Saturday.