Santa Cruz play and were aware of his professionalism. 2006 FIFA World Cup Santa Cruz was in doubt for the 2006 World Cup as he had been recovering from a knee injury, however, he recovered in time for the start of the tournament and was eventually was selected in the 23-man squad by coach Aníbal Ruiz. Despite wearing the number 24 shirt during the World Cup qualification campaign, he was handed the number 9 for the tournament. Santa Cruz was part of the starting XI players in Paraguay's first match against England on 10 June. He was partnered upfront alongside Nelson Valdez in the eventual 1–0 loss. Santa Cruz again started in Paraguay's 1–0 loss to Sweden on 15 June, where he was substituted off of the field for Dante López in the 63rd minute. Santa Cruz played a full 90 minutes of Paraguay's third group stage match against Trinidad and Tobago on 20 June, he had assisted Nelson Cuevas with a pass in scoring Paraguay's second goal in the 86th minute of the 2–0 victory. Paraguay finished in third position of their respective group, obtaining three points for their win against Trinidad and Tobago. 2007 Copa América Santa Cruz was selected for the 2007 Copa América under new coach Gerardo Martino. In Paraguay's first group stage match against Colombia on 28 June, Santa Cruz scored a hat-trick in his side's 5–0 victory. His first goal was a left-footed chip in the 30th minute, his second goal was a right-footed shot in the 46th minute assisted from an Édgar Barreto pass, and his third goal was a header in the 80th minute assisted from a cross by Carlos Bonet. Santa Cruz played a full 90 minutes of Paraguay's 3–1 victory against the United States on 2 July. Santa Cruz was substituted onto the field for Jonathan Santana in the 81st minute of Paraguay's last group stage fixture, a 1–0 loss against Argentina on 5 July. Paraguay had finished in second place of their respective group, having obtained six points from their two wins. They advanced to the quarter final stages where they faced Mexico on 8 July, where Santa Cruz played a full 90 minutes of Paraguay's 6–0 loss. 2010 FIFA World Cup Santa Cruz scored three times during qualification for the 2010 World Cup, including the opening goal of a 2–0 defeat of Brazil in Asunción, as La Albirroja