Canada 0 Colombia 1: Rodriguez the hero for Pekerman's men
Canada were resilient and compact throughout against a superior Colombia side but they were eventually breached by James Rodriguez with 16 minutes remaining at Red Bull Arena in New York.
The Real Madrid star was fouled and collected a quickly taken free-kick before firing the ball into the corner of the net as Colombia made it back-to-back wins in the USA after disposing of El Salvador on Friday.
Five changes were made to the Colombia team that beat El Salvador 3-0 last week, with Cristian Zapata, Camilo Zuniga, Jeison Murillo, Juan Cuadrado and Teo Gutierrez called up by Jose Pekerman.
Adam Straith, Nik Ledgerwood and Pedro Pacheco took to the field as Canada made three changes in the country's first match since accounting for Jamaica 3-1 last month.
Colombia, as expected, dominated proceedings for large periods, though Canada had a penalty turned down early on.
After a great ball from Issey Nakajima-Farran, Tosaint Ricketts was bundled down inside the area in the fifth minute but Canada's appeals fell upon deaf ears.
Up the other end, Colombia were unfortunate to be denied a 20th-minute opener.
Captain Radamel Falcao found the back of the net but the flag was raised for offside following a neat one-two between Gutierrez and Rodriguez.
Rodriguez came close to breaking the deadlock three minutes before half-time, but Canada goalkeeper Milan Borjan was up to the task, pushing the Real Madrid star's free-kick away for a corner.
Colombia piled on the pressure in the second half, with Zuniga and Gutierrez coming close against an organised Canadian defence.
Cuadrado also tried his luck from distance, forcing Borjan into a diving save as his shot dipped towards the bottom corner.
Growing frustrated and with time running out, Rodriguez finally made the breakthrough after 74 minutes, unleashing a powerful shot into the top corner.