Only 4 minutes after Venegas replaced Patrice Bernier, the Costa Rican won a battle for the ball with Michael Parkhurst and went in on a 2-on-1 with Montreal star Didier Drogba. Venegas elected to shoot and picked the far corner for the winner.
The second leg of the two-game, total-goals series is next Sunday in Columbus.
Bernier also scored for Montreal, coming off a 3-0 home victory over Toronto FC in a knockout game Thursday night.
Federico Higuain opened the scoring for the Crew in the 33rd minute. Bernier tied it in the 37th on a header off Marco Donadel's corner kick.