Substitute striker Lucas Barrios scored in the 90th-minute to cap Paraguay’s comeback after Argentina had opened a two-goal lead in the first half.
Sergio Aguero opened the scoring for Argentina in the 29th after intercepting a bad pass by Paraguayan defender Miguel Samudio, and Lionel Messi added to the lead by converting a 36th-minute penalty after Samudio was called for a foul on Angel Di Maria.
Paraguay scored its first goal with Nelson Valdez’s shot from the top of the area in the 60th, and Barrios equalized with a left-footed shot after a long cross into the area. The ball was deflected back toward Barrios and he quickly fired his shot low into the back of the net as Argentina goalkeeper Sergio Romero could only watch.
“We showed that we are a strong team,” said the Argentine-born Barrios, who celebrated by taking off his jersey and running toward his teammates.
Argentina dominated most of the match at the La Portada Stadium and seemed headed to an easy victory in its opener, but Paraguay surged forward after scoring its first goal and created several opportunities until finally equalizing with Barrios.
“We had the match under control,” Argentina coach Gerardo Martino said. “But we made too many mistakes in the second half.”
Argentina, trying to end a 22-year title drought, missed a chance to reach the top of Group B along with Uruguay, which earlier Saturday defeated Jamaica 1-0 in Antofagasta.
“It’s upsetting to end up with the draw after being up 2-0,” Messi said.
Aguero put Argentina ahead after Samudio’s pass back to goalkeeper Antony Silva was short, allowing the striker to enter the area free from any defenders and in great position to score. He easily cleared the goalkeeper before finding the open net with a right-footed shot.
Messi converted the penalty with a firm low shot into the corner, scoring his 46th goal in 98 matches with the national team. Paraguayan players complained with Colombian referee Wilmar Roldan, saying Samudio made a clean challenge on Di Maria in the play that prompted the penalty.
Paraguay pressed forward after Valdez scored his goal with a shot over Romero. Valdez nearly equalized in the 71st with a close-range shot that missed just wide, and Samudio had his shot stopped by Romero in the 76th.
“After the first goal they began to play well and we didn’t have an answer to their game,” Argentina midfielder Javier Mascherano said.
Argentina hasn’t won a significant trophy since the 1993 Copa America in Ecuador, when Messi was only six years old.
The Argentines hosted the 2011 Copa America, but Messi and his teammates were eliminated by eventual champion Uruguay in the quarterfinals. Argentina lost consecutive finals to Brazil in 2004 and 2007.
Argentina next play Uruguay in La Serena, while Paraguay will face Jamaica in Antofagasta. Both matches will be on Tuesday.