The teams ended 1-1 on Friday and couldn't be separated after the first five spot kicks either until Wilker Angel saw his sudden death spot-kick saved by Maxime Crepeau.
Ismael Kone then buried the winning penalty to send Canada through.
Canada will face Argentina in New Jersey on Tuesday for a chance to play in the July 14 final. The semi-final will be a rematch of the tournament's opener, in which defending champions Argentina claimed a 2-0 win.
Canada, who scored just one goal across their three group stage matches, began with uncharacteristic urgency and their pressure paid off in the 13th minute when Jacob Shaffelburg steered home a Jonathan David cross.
Jesse Marsch's side wasted several chances to extend their lead in the first half, with Shaffelburg testing goalkeeper Rafael Romo from the edge of the area while David sent an effort wide of the post after finding himself through one-on-one.
Venezuela pressed for a goal and had more possession, but were largely limited to speculative crosses and shots from range, with all-time leading goalscorer Salomon Rondon twice drawing saves from Canadian No.1 Crepeau.
Canada's Cyle Larin fired over the bar from close range in the 52nd minute. Two minutes later, a rebound fell at the feet of Venezuela's Jose Martinez in the penalty area at the other end, but his effort also went high.
Venezuela finally found the equaliser in the 64th minute through Rondon, who spotted Crepeau off his line and produced an audacious lob that sailed over the scrambling goalkeeper into the empty net.
It was the former Everton and Newcastle United striker's 44th goal for Venezuela.
Canada responded well to the equaliser and substitute Liam Millar had an effort from a tight angle saved in the 67th minute before Tani Oluwaseyi sent two shots over the crossbar in the span of four minutes.
But neither side could produce a winner in regulation time which forced the shootout.
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