Gutierrez broke the deadlock just before halftime at the Campin on Thursday night by latching onto a Jarlan Barrera through ball and dribbling past goalkeeper Robinson Zapata to fire into an empty net, reports Xinhua.
Piedrahita doubled the visitors' lead five minutes after the restart, lashing in from a tight angle after Luis Diaz's deft control and lay-off.
Santa Fe were reduced to 10 men in the 85th minute when Javier Lopez was shown a straight red card for hacking down Jarlan Barrera.
The return leg will be played in Barranquilla on November 30.
Brazilian rivals Atletico Paranaense and Fluminense are contesting the other semi-final, with the former having secured a 2-0 home victory in Wednesday's first leg.
The winner of the Copa Sudamericana will earn a berth in next year's Copa Libertadores, South American football's top club tournament.
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