Otamendi played the full 90 minutes in Salvador while Aguero figured for 79 minutes before being replaced by Matias Suarez
Argentina, aiming to win the Copa America for the first time since 1993, had dominated the clash with Lionel Messi heading their best chance wide after Colombia keeper David Ospina had saved from Otamendi.
However, somewhat against the run of play, Colombia – managed by former Real Madrid, Poertugal and Iran boss Carlos Quieroz - struck twice in the last 20 minutes.
On 71 minutes Roger Martinez fired an impressive effort into the top corner of the net to give Colombia the lead.
And with time almost up Duvan Zapata struck from close range to leave La Albiceleste stunned and throw Group B wide open.
Argentina next face Paraguay, who begin their campaign against invitees Qatar later tonight (8pm).