Colombia played some sparkling, attacking football at times as they comfortably beat the CONCACAF champions in front of a lively 51,000 crowd at the home ground of the NFL's Miami Dolphins.
Colombia grabbed the lead in the 37th minute when a low shot by Dorlan Pabon was pushed out by Mexico goalkeeper Guillermo Ochoa and Radamel Falcao pounced to slot home.
Mexico's Manchester United striker Javier Hernandez had a chance just before the interval but was forced wide and the main threat for 'El Tri' had few other opportunities.
The impressive Juan Guillermo Cuadrado went close after the restart with a fierce shot after a fine solo run but it was not long before Colombia doubled their advantage.
James Rodriguez fed Pablo Armero, who burst down the left flank and then delivered a pinpoint low cross for Cuadrado to slide in at the back post to make it 2-0 in the 60th minute.
From then on Colombia, playing with real fluency and pace, enjoyed plenty of midfield possession while Mexico laboured to try and get back into the game.
Pekerman was delighted with the way his team had responded to his request for them to play a high-tempo, positive style and to work hard when the opposition had the ball.
"We believe in the players, we had seen from the outside, before we took over, that this team had possibilities," he said.
"I had the feeling tonight that the team was really balanced, the players put in a lot of effort and we saw the attacking players working hard when they didn't have the ball.
"It's good to know we can do these things, we adapted well when they had the ball."
Hernandez said Mexico, who have been in impressive form of their own since Jose Manuel de la Torre took over and led them to last year's CONCACAF Gold Cup, needed to draw some lessons from the loss.
"It was a very tough game, we are obviously saddened by the loss but whether we win, lose or draw, we have to keep on improving. It is different to learn from a win or a defeat - we have to learn from this 2-0.
"The coach told us we have to keep on working, it doesn't mean the end of anything, we have to be a little bit more consistent, but we were facing a very formidable opponent, we always trying to impose ourselves but sometimes you come up against a team that dictates the game."
