the qualification campaign for the 2002 FIFA World Cup, Santa Cruz had scored a total of three goals. His first goal came in round nine, when Santa Cruz had scored Paraguay's first goal in the third minute of a 2–0 away victory against Colombia on 7 October 2000. His second goal came in a 5–1 home victory against Peru on 15 November 2000, and Santa Cruz scored his third goal of the 2002 World Cup qualification in a 5–1 home victory against Bolivia on 5 September 2001. Prior to the World Cup, Santa Cruz scored his eighth international career goal in a 2–1 victory against Sweden in a friendly on 17 May 2002. Santa Cruz scored four goals during the qualification campaign for the 2006 World Cup. His first came in a 2–1 home victory against Ecuador on 15 November 2003, when Santa Cruz had given Paraguay a 1–0 lead in the 29th minute. Santa Cruz then scored Paraguay's only goal in their 4–1 away loss against Brazil on 5 June 2005. Three days later, Santa Cruz scored his third goal of the qualification campaign in a 4–1 home victory against Bolivia in Asunción on 8 June 2005. In round 16 of the qualification campaign, Santa Cruz scored in the 14th minute of the 1–0 home victory against Argentina in Asunción on 3 September 2005. His four goals during the qualification campaign brought him to a tally of 13 international goals for Paraguay. Santa Cruz did not score his next international goal until two years later, Paraguay's only goal in their 2–1 away victory against Mexico at the Estadio Universitario in Monterrey on 25 March 2007. During the qualification campaign for the 2010 World Cup, Santa Cruz had scored three goals for Paraguay. His first goal came in the 50th minute of a 5–1 home victory against Ecuador on 17 November 2007, Santa Cruz had dribbled into the 18-yard box and scored with a right-footed shot. On 15 June 2008, Santa Cruz scored Paraguay's first goal in their 2–0 home victory against Brazil in Asunción, hitting a far-post tap-in, side footing the ball into the net after receiving it from a corner. Then, in the 49th minute, he received a through ball from Nelson Valdez and dribbled towards the goal to attempt a shot on goal. His shot was initially saved by Brazil goalkeeper Júlio César, but fell into the