Venezuela had already booked their spot in the last eight with wins over Ecuador and Mexico and needed just a point against already eliminated Jamaica to clinch top spot and avoid facing defending champions Argentina in the next round.
Eduard Bello's powerful downward header put the South Americans in front in the 49th minute, and Salomon Rondon doubled their lead seven minutes later with a scuffed effort past Jamaica keeper Jahmali Waite.
Eric Ramirez added the third on the breakaway in the 85th minute.
Venezuela were joined in the last eight by Group B runners-up Ecuador, who qualified thanks to their superior goal difference after holding Mexico 0-0 in the other match in Glendale, Arizona, with both teams tied on four points.
The result also means Mexico bowed out of the tournament after finishing third in Group B.
Ecuador face defending champions Argentina in the quarter-finals.
In a physical first half, Mexico attacked with real intensity as they sought the win they needed, but they lacked quality on the ball and failed to record a shot on target.
Jaime Lozano's side continued to push after the break and Gerardo Arteaga was denied by a last-ditch tackle from Felix Torres, while Julian Quinones tested Ecuador's Alexander Dominguez with a long-range effort.
Mexico continued to throw bodies forward in their search for a winner and were awarded a penalty when Torres appeared to bring down Guillermo Martinez, but the decision was overturned after a VAR review.
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