The visitors dominated the first half and went into the break with a 1-0 lead given to them by Alvaro Morata in the 32nd minute at the near post.
Massimiliano Allegri's side continued to look comfortable after the interval, but they could not make their pressure count as a second goal remained elusive.
Their profligacy in front of goal proved costly as, against the run of play, Mattia Aramu arrowed an equaliser into the bottom corner in the 55th minute to stun Juve.
The chances continued to come and go but Allegri's men could not find a winner, with the draw meaning Juve fell to sixth in the standings, 10 points off leaders AC Milan, who play later on Saturday.
Newly-promoted Venezia, who avoided defeat for the first time in four league games, stay 16th on 16 points from 17 games.
"These are two points thrown away against an excellent Venezia," Allegri told DAZN. "The first half we did well, creating many chances on goal. Then there was a blackout of 10-15 minutes until the goal of Venezia.
"There are times where we are beautiful, but when you have to grit your teeth we don't."
Juve came into the contest in good form, having won their previous three games in all competitions without conceding a single goal.
They soon exerted some control on the match in Venice, even though they were dealt an early blow after forward Paulo Dybala was forced off with an injury.
Morata, who has received criticism from his own fans for his performances this season, then edged his side in front with his fourth Serie A goal of the campaign, on the end of a Luca Pellegrini cross.
Armu's equaliser from 20 metres out pegged Juve back, with the Old Lady looking less of a threat in the latter stages in the match.
They did, however, muster 20 shots at goal in the match, with their finishing, not for the first time this season, letting them down as Venezia celebrated a point against Serie A's most successful side.