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 is now unbeaten in 15 league games, although it missed a chance to extend its advantage at the top of Serie A after Roma was 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 6 yards.
Verona put together some neat passing moves as it 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 through ball from Paul Pogba, and fired through Rafael's legs from close range.
Juventus was in complete control for the remainder of the first half, denying its host a shot on target.
Verona finally got itself into the game after the interval and halved the 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 ruled offside before squaring to the striker.
Buffon made a late save to deny Toni a second goal, before Juve center back Giorgio Cheillini limped out of the match with 15 minutes remaining because of 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 equalizer.