Dusan Vlahovic earned disappointing Juve a point with a bullet header with 10 minutes remaining at the Allianz Stadium after Lewis Ferguson had put Bologna ahead midway through the first half.
But they were fortunate not to lose as referee Marco Di Bello decided not to award a spot-kick to Bologna after Dan Ndoye was brought down by Samuel Iling-Junior nine minutes before Vlahovic levelled.
It was a decision which so angered Bologna that it prompted a livid post-match reaction from the club's CEO Claudio Fenucci as coach Thiago Motta refused to talk to media.
"I've done this job for 25 years and I don't often go on TV to talk about referees," said Fenucci.
"The win was taken from us by an incredible refereeing decision... It's unthinkable that a challenge like that is not punished with a penalty and a red card."
It was an uninspiring display from Juve which poured cold water on the idea that they are back as league title contenders.
Massimiliano Allegri's side impressed at Udinese last weekend, not just with the win but with their aggressive, attacking style of play.
But on Sunday Juve were back to the stodgy ways of last season which so angered supporters.
- Juve booed -
Not even the return of Paul Pogba to midfield could inspire Juve to claim the three points, the France star doing little as a second half substitute as Juve huffed and puffed ineffectively.
Juve were booed off after a dismal first half which featured just one shot on target from the home side and none of the verve which characterised last weekend's win.
Bologna were the more dangerous side and were deservedly ahead in the 24th minute through Ferguson who slotted home a perfect low finish after being brilliantly slipped through by Joshua Zirkzee.
Dutch attacker Zirkzee was involved again when Ferguson came close to doubling the away side's lead, feeding the Scotland midfielder before another low effort grazed the upright.
Juve came out with more aggression after the break and Vlahovic soon thought he had equalised with a smart volleyed finish, only for it to be chalked off for Adrien Rabiot straying offside and blocking the view of Bologna goalkeeper Lukasz Skorupski.
But the match turned on the key penalty decision in the 71st minute.
Bologna coach Thiago Motta was booked and one of his assistants sent off as they looked on in disbelief after on-field and VAR officials allowed Iling-Junior to cut down Ndoye to stop him from tapping in from close range.
Worse for the away side was that the English winger supplied the cross from which Vlahovic headed Juve level with 10 minutes remaining, but they held out for a creditable point.
- Lecce bounce back -
Fiorentina looked set for a simple win in Florence when headers from Nicolas Gonzalez and Alfred Duncan had the hosts two goals to the good at half-time.
And Nikola Krstovic earned the away side a dramatic point when he evaded two Fiorentina centre backs to head home Lameck Banda's inswinging cross.
Vincenzo Italiano's Fiorentina now face the second leg of his team's Conference League play-off with Rapid Vienna on Thursday with the Tuscans trailing by a single goal.