Santa Cruz helped his side move in sight of the second phase with a 2-0 victory against Slovakia at the Free State Stadium. Goals from Enrique Vera and Cristian Riveros either side of half-time gave them victory after they drew their opening game with reigning world champions Italy.
The Italians could then only draw with New Zealand meaning Paraguay now need only one point from their final game against the All Whites to advance. Santa Cruz believes the bond between the players is key to the team's achievements.
He said: "We controlled the game and are happy to have achieved our goal of getting the points. Our strengths are as a team we are very compact. We are all proud to be part of the squad. The atmosphere is fantastic, not just in our games but in training. We have been playing together for years and we have players who are mentally strong. Our strength is the spirit in the camp, the hard work we put into every game."
The Manchester City striker came up against club team-mate Vladimir Weiss yesterday and exchanged shirts with the 20-year-old before tipping him for a bright future. Then the winger's father - the Slovakia coach of the same name - took time out to greet Santa Cruz as he was being interviewed to give him a hug.
Santa Cruz continued: "I know Vladimir very well from our time City. He is a fantastic guy, a great player. I am pleased to see him doing well in his national team."
Santa Cruz, back in the side after a minor injury, called on his team to make history. "Paraguay have never been in the quarter-finals. That is our goal," he added. Maybe it is time to change history. We are very proud of our result. It will give us a lot of confidence. It is very important we win our last group game. There is a possibility we could top the table and we have to go for it. If we keep working hard who knows how far we can go."
Slovakia are in the finals for the first time and coach Weiss refused to be downbeat. He said: "It is a good learning experience for my team and we are happy to be at the World Cup. We made two mistakes and were punished for them. There was not enough urgency in our play."