Paraguay, Uruguay and Chile, who finished behind Colombia in that order in the six-nation title group on Sunday, will join the winners in the Under-20 World Cup in Turkey from June 21 to July 13.
Colombia's outstanding player, Juan Fernando Quintero of Italy's Pescara, put his team ahead with his fifth goal of the tournament and centre back Jherson Vergara headed the second. Midfielder Jorge Rojas pulled back a late goal for Paraguay.
Outgoing champions Brazil and hosts Argentina, who between them have won 11 under-20 world titles, failed to qualify for the final group.
It was Colombia's first success away after they won the title at home in 1987 and 2005.