Bolivia soaked up the pressure in the first half before snatching the lead early in the second through Edivaldo Rojas. The hosts had to wait until the 77th minute for the equaliser when Aguero slammed the ball home.
Argentina's Lionel Messi was marked tightly by the Bolivian defense and had few chances to shine.
"It is not what we expected, now we must improve and we win our remaining [group] matches," a visibly disappointed Messi told reporters. "Now we need tranquility."
Having weathered a first-half storm at the Ciudad de La Plata stadium, Bolivia stunned Argentina two minutes into the second half when Jhasmany Campos hit a corner low to the near post where Rojas back-heeled it past goalkeeper Sergio Romero.
Marcelo Martins looked set to give Bolivia a two-goal lead on the hour when he beat Argentina's offside trap but Romero dived to touch the ball away from the striker's feet then got up to block his second effort.
"We had a couple of situations that if we'd put them away we could have won the match," Bolivia's Argentine-born coach Gustavo Quinteros said.
"I think the team settled and were more solid in the final minutes of the first half and almost all of the second," he told news conference.
"For us, after such a short time working together and few matches, this is a good result that motivates us to carry on."
ONE-WAY TRAFFIC
Argentina equalised with 13 minutes left when Nicolas Burdisso chested down a cross from Marcos Rojo and Aguero volleyed home. Minutes after his goal, Aguero might have snatched a win for the hosts but his shot brought a diving save from Bolivia goalie Carlos Arias.
The draw was a positive result for Bolivia, said goalscorer Rojas.
"This result is very important psychologically for our next match [against Costa Rica]," he told a news conference.
While the first half was dominated by Argentina, the only shot on target came from the ultra defensive Bolivians' single chance when Martins squared the ball to Rojas and his weak but well-directed shot was saved by Romero.
Apart from that chance it was almost one-way traffic towards the Bolivia box with Argentina winning a string of corners but failing to get a clean shot on target.
The hosts almost broke through when striker Ezequiel Lavezzi broke in from the right and sent a low shot just wide of the far post. Messi then linked with Carlos Tevez but the moved fizzled out for a corner, and midfielder Esteban Cambiasso was unable to capitalise on a loose ball after a jinking Messi run.
In an exciting finish, either side could have snatched victory as Argentina created chances while Bolivia attempted to hit them on the break.
