Despite a shoulder injury Colombian star James Rodriguez played through the pain and helped set up his side's first goal with a corner kick in the 12th minute. He then scored what proved to be the game winning goal 18 minutes later.
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Victor Ayala got Paraguay on the board with a jaw-dropping strike in the 71st minute, but his team couldn't find an equalizer.
Paraguay drew 0-0 with Costa Rica in an uninspiring game on Saturday. Paraguay Manager Ramon Diaz believed his side deserved to win against Costa Rica.
Colombia made the Copa America quarterfinals in last year's tournament. Paraguay made the semifinal last year.
Colombia has been listed as one of the favorites for the tournament alongside Argentina and last year's champion Chile.