Sergio Aguero opened the scoring against Paraguay after half an hour and when Lionel Messi added a second from the penalty spot it looked as if La Albiceleste would easily claim all three points, but their opponents fought back after the break to ensure it finished 2-2.
Considered one of the favourites for the tournament after going all the way to the World Cup final in 2014, Argentina are looking to lift a first Copa America trophy in 23 years and they got off to the best possible start when Aguero seized on an undercooked back pass and slid the ball beyond the reach of keeper Antony Silva.
Under 10 minutes later Messi doubled the advantage from 12 yards after Angel Di Maria was fouled in the box and he might have made it three, only denied by the legs of Silva.
Yet the Argentines were unable to translate their first half dominance into a third goal, despite running the Paraguay defence ragged who appeared to have no answer to the attacking triumvirate of Aguero, Messi and Di Maria.
However, on the hour mark Nelson Valdez brilliant effort gave Paraguay a lifeline and for the last half hour the game was a much more even affair.
Even so, it looked as if Argentina had survived the danger intact when Lucas Barrios converted from an 89th minute free kick to break Argentinian hearts and spark wild celebrations across Paraguay.
Kun was withdrawn after 76 minutes for Gonzalo Higuain as Gerardo Martino introduced some fresh legs from the bench while former Blue Carlos Tevez came on for Javier Pastore with 10 minutes to go as the Argentines kept focus on attack.
Martin Demichelis and Pablo Zabaleta were both unused substitutes for this opening encounter but will hope to see some action when Argentina take on Uruguay on Wednesday.
This result leaves them two points behind the defending Champions who surged ahead in the group with victory over Jamaica.
