"I'd like to congratulate the whole of Colombia because they deserved this," Pekerman told FIFA.com. "We made some alterations because we knew how strong our opponents were - it's really important to know about the opposition.
"The main factor was the first half, when we were very solid and managed to get ahead. It's great to have a player like James Rodriguez, and his confidence was very high after our previous game."
Colombia will now face hosts Brazil for a place in the semi-finals.