Antonio Conte's side looked to be on course for all three points after Carlos Tevez scored twice, only for the striker to strike in the fourth minute of injury-time
Carlos Tevez struck twice in the first half to put the visitors in complete control, with the 30-year-old taking his tally for the season to 13 with two close-range finishes.
Former Juventus forward Luca Toni pulled a goal back seven minutes after the break, and with time running out the Argentine substitute rose to meet a Romulo cross and head past Gianluigi Buffon.
Despite the disappointment, Juve are now unbeaten in 15 league games, although they missed a chance to extend their advantage at the top of Serie A after Roma were held by Lazio in the Rome derby.
The visitors, who welcomed Buffon back after suspension, started at a high tempo and were rewarded with the opening goal in the fourth minute.
Kwadwo Asamoah raced past Fabrizio Cacciatore on the left and saw his low shot parried by Rafael, before Tevez latched onto the rebound to find the net from six yards.
Verona put together some neat passing moves as they looked to respond, but more slack defending in the 21st minute allowed Tevez to double his tally.
The Argentina international sprung the offside trap to receive a perfectly weighted throughball from Paul Pogba, and fired through Rafael's legs from close range.
Juventus were in complete control for the remainder of the first half, denying their hosts a shot on target.
Verona finally got themselves into the game after the interval and halved their deficit in the 52nd minute through Toni’s sixth goal in his last six league appearances.
Romulo delivered a free-kick to the near post for the striker, who got ahead of Leonardo Bonucci and headed low past Buffon.
Pablo Daniel Osvaldo was handed his debut midway through the second half and the Southampton loanee had an immediate impact.
He saw a low shot clip the post on its way wide, and had a goal disallowed soon after as Asamoah was adjudged offside before squaring to the striker.
Buffon made a late save to deny Toni a second goal, before Juve central defender Giorgio Cheillini limped out of the match with 15 minutes remaining due to an apparent calf injury.
Verona subsequently saw a penalty shout turned away as Stephan Lichtsteiner appeared to handle the ball inside his own penalty area when challenging Toni.
However, it did not matter as Juanito rose highest to head home a dramatic equaliser.