Massimiliano Allegri's men had won three games in a row without conceding in all competitions ahead of the trip to Stadio Pier Luigi Penzo, but they were unable to hold on to a first-half lead given to them by Alvaro Morata.
Juve, which lost Paulo Dybala to injury inside 12 minutes, was pegged back by a long-range strike from former Torino midfielder Mattia Aramu 10 minutes into the second half.
The visitors were unable to hit back against a Venezia side that had lost its past three games and conceded 10 goals in the process, placing it six points behind fourth-placed Atalanta, which faces Hellas Verona on Monday (AEDT).
Dybala's replacement Kaio Jorge flicked over from close range and Morata's drive forced a good save out of Sergio Romero before the Spain international managed to find a way through with 32 minutes played.
Luca Pellegrini sent a low cross in from the left and Morata got in front of his marker to flick the ball past Romero, the goal allowed to stand after a VAR (video assistant referee) check for a possible handball from Federico Bernardeschi in the build-up.
Juan Cuadrado wasted a good chance when firing across the face of goal shortly before the interval and Juve were made to pay as, after a spell of Venezia pressure, Aramu curled in a low first-time shot from range.
Allegri's side failed to create much in way of response, with one shot on target in the second half summing up its struggles as the contest finished all square.