With a place in the 2014 Copa Sudamericana on the line, Palestino made the perfect start to their semi-final tie.
Renato Ramos' 49th-minute goal was all they needed to win at Cobreloa's Estadio Regional Calvo y Bascunan.
In the other semi-final, Cobresal were held to a 0-0 draw at home to Universidad Concepcion.
Emiliano Astorga's Palestino are well-placed heading into the second leg thanks to Ramos' goal in Antofagasta.
The second legs of both ties will be played on Sunday.
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