Luigi Del Neri's side throw away advantage in front of their own fans with Fernando Uribe and Gennardo Sardo grabbing the decisive goals for the visitors at the Olimpico
The legendary captain celebrated his new one-year contract extension when he scored from the spot just 13 minutes in and Matri gave his side some breathing space as he stroked the ball into the back of the net soon after the restart.
However, Chievo responded following some slack defending from the home side as Fernando Uribe cut the deficit, scrambling home when the hosts' defence fell asleep from a free-kick.
Juve lights then went out completely as the away side came to life when Sergio Pellissier hit the post, but Gennardo Sardo did not miss from close range as he equalised from the rebound.
Luigi Del Neri's men started well as Del Piero turned the ball to Fabio Grosso on the flank. The Italian drove into the box in search of Matri, but the Chievo defence scrambled clear.
Chievo were never too frightening for Juve, but sloppy play from Alberto Aquilani allowed Sergio Pellissier a great chance to scare them early as he turned and shot although he was closed down as Giorgio Chiellini reacted well.
Juventus were dangerous down the flanks and it showed when Pepe was brought down inside the box following a cross from Milos Krasic.
The referee deemed Sardo's pull on his shirt enough to warrant a penalty and Del Piero made no mistake as he hit the top corner to give his side the lead.
It could have been more minutes later when Aquilani tried to chip Stefano Sorrentino from outside the area, but the goalkeeper tipped over the bar.
The on-loan Liverpool midfielder should have buried from just yards out soon after, but he sent Marco Motta's cross woefully over.
Bojan Jokic cut inside and curled a right-foot effort towards goal, but Gianluigi Buffon made the save as Chievo made a rare foray forward.
Chievo were sleeping at the back, and were lucky not to give away a second penalty. Del Piero fed Grosso who went down, but it was just on the edge of the area.
Del Piero took the resulting free-kick and went for the near post, but it was headed clear by Marco Andreolli.
Pepe, the match winner against Lazio last week, almost made his mark when meeting a Krasic cross, but his headed effort was just over.
Motta did fantastically well to get down the line and hold up a ball for Krasic inside the area. The Serbian knocked it back for Matri who turned, only to find Del Piero in his way as the chance was cleared by Andreolli.
Matri soon put more space between Juve and Chievo as Del Piero slid the ball into his path before he controlled and buried past Sorrentino.
Chievo appeared dead and no-one would have believed in them getting anything from the game, but Juve's lax approach after going two up backfired badly.
Uribe latched onto a free-kick after Gianluigi Buffon failed to save and bundled the ball over the line.
The Bianconeri never recovered from the shock and drifted away as roles were reversed. Sardo then made up for his earlier error as he smashed the ball into an empty net after Pellissier hit the post.
In a frantic finale Luca Toni hit the woodwork for Juve, while Uribe failed to score down the other end after Buffon left his net unguarded. Marchisio cleared off the line to spare the Italian goalkeeper's blushes. But, by that point the damage had been done.
Juve now stand little chance of gaining a place in next season's Champions League while Chievo climb to 12th.