The visitors scored on each side of half-time to help get a win for the new boss, who was hired by the team earlier this year
Radamel Falcao opened the scoring just past the midway point of the first half, and Juan Cuadrado gave Colombia the two-goal cushion with a half-hour to play.
Mexico opened the night on the move, forcing goalkeeper David Ospina into some tough saves early on. In two instances in the opening 20 minutes Ospina took a knock after colliding with Mexico's attacking players. He also watched a shot bounce off the post.
Despite this pressure it would be Colombia - which hired Pekerman in January - who struck first.
While the Cafeteros did not enjoy much possession in the first half, on the counter attack the South Americans were always a threat. The visitors took advantage of one of their few scoring chances in the first half Mexico keeper Guillermo Ochoa parried an effort in the 37th minute.
Falcao put Colombia ahead on a poacher's effort after Cuadrado's shot bounced off Ochoa. The sequence was launched by a free kick from James Rodriguez.
Right before the half it appeared as though Javier Hernandez was ready to give El Tri the goal they have been looking for as he had a wide-open net to simply tap the ball in. But despite getting behind the defense and keeper, Chicharito was unable to gain full control.
The second half began much like the first, with Mexico looking like the stronger team offensively. And just like in the opening 45 Colombia put the ball in the net, leaving Mexico shocked.
In the 60th minute, Cuadrado was on the receving end of the ball as he converted a perfectly placed cross from Pablo Armero. Rodriguez initially set up the play on the left side of the pitch and Ochoa had no chance of stopping the storming midfielder.
Chicharito left the action in the 73rd minute and Mexico were unable to cause any major threats as the game wound to a close, ending what was a disappointing start to their 2012 season.