Castellanos, who joined City from Atletico Madrid this summer, was a constant threat throughout the game and was denied a first-half goal by a last-ditch block as she went through on goal.
After the break, Castellanos fired an angled shot just wide of the post after some neat build-up play on the edge of the box.
The 23-year-old skipper saw another shot clear the bar after turning a defender on the edge of the box, before scoring what proved to be the only goal of the game on 78 minutes – and what a strike it was.
Venezuela were awarded a free-kick 25 yards out in a central position.
Castellanos stepped up and fired a thunderous rising shot that skimmed the underside of the bar on its way into the back of the net to deservedly win the game for the Venezuelans who are now joint top of Group B with Brazil, who lead on goal difference with one game played.