Paraguay stunned the twice world champions with a fast break from deep in their own half, Angel Romero playing the ball into the path of Derlis Gonzalez, who beat Sergio Romero with a shot inside the near post in the 18th minute.
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The defeat left Argentina, who dropped seven points in three successive matches without Messi, in fifth place in the South American group with 16 points, one point ahead of Paraguay who had never won a qualifier in Argentina before.
Argentina could have got back on level terms two minutes into the second half, but Paraguay captain Justo Villar saved Sergio Aguero's weak penalty. "There are no excuses, we played badly," Aguero told reporters. "We've got to pick ourselves up... turn everything around."
Paulo Dybala, who came on in the second half to try and bring more creativity to the team, was also unimpressed. "It's a bad moment. We've got to try to get out of this rut in the next matches," he said. "A national team like ours has to participate in the World Cup."
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Argentine defence with little or no club action this season, had the ball in the Paraguay net at a free kick in the second half but the referee ruled it offside. In the first half, Angel Di Maria hit the Paraguay post with a shot across the face of goal.
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