The Black Stars will now take on Uruguay.
Goals from Kevin-Prince Boateng and Asamoah Gyan saw the Black Stars overcome the Stars and Stripes.
"Ghana is now among the best eight teams in the world," Serbian-born Rajevac told the Canadian Press after the match. "The whole world is watching these games.
"I said that everybody loves good football on each continent. So, at the moment Ghana has the support of the world.
"I have to congratulate my players. They had the force and the strength to go to the end and win."
"During extra time, we needed the strength and we were able to find it," he added.
Ghana will now take on Uruguay in the quarterfinals on Friday.
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