The Scottish league leaders' hopes of qualifying for the last eight all but disappear as the Turin giants score through Alessandro Matri, Claudio Marchisio and Mirko Vucinic
Despite dominating the majority of the game, the Scottish champions were unable to find a way back into the game and must now claim victory in Turin to qualify for the quarter-finals.
Neil Lennon made nine changes from the weakened side that claimed victory at Inverness CT on Saturday, with Fraser Forster and Kris Commons remaining in the team, while there were recalls for James Forrest from injury and Efe Ambrose, who surprisingly started just two days after winning the Africa Cup of Nations with Nigeria.
The visitors made two changes from their win over Fiorentina, with Paolo De Ceglie and Luca Marrone dropping out to be replaced Martin Caceres and Leonardo Bonucci while Nicolas Anelka found a place on the bench.
Celtic looked to give the home support something to cheer about in the opening minutes but, after Gianluigi Buffon tipped over Victor Wanyama's long-ranger, disaster struck with only three minutes on the clock.
Profiting from a long ball, Matri got in behind Ambrose and smashed an effort towards goal. It looked to have crossed the line before Kelvin Wilson cleared but Marchisio made sure the ball was over, rifling it into the back of the net, though the goal was credited to the forward.
From then on the home side dominated the first half, with Emilio Izaguirre finding Commons twice with crosses from the left wing, but on both occasions the Scotland international failed to find the target.
Juventus did have an opportunity on the break to double their lead as Vucinic rounded Forster after getting onto a long ball but the striker found himself at too acute an angle to find the target and Celtic cleared, while Commons continued to get the chances for the SPL leaders as he tried an overhead kick from a Mikael Lustig cross.
Closing in on the hour mark, Celtic fans were up in arms looking for a penalty as Forrest went down under a challenge from Andrea Barzagli but the referee waved away the complaints.
The Parkhead outfit should have got level as Commons played a corner from the left short to Charlie Mulgrew and he swung in a teasing cross right onto the head of Ambrose but the Nigerian international somehow directed the ball straight at Buffon.
Despite dominating the fixture, Celtic soon found themselves two goals behind after a superb passing move ended with Matri finding Marchisio, who rounded substitute Adam Matthews and placed the ball beyond Forster to secure the victory.
The tie was effectually over as Ambrose lost possession on the edge of his own area to Marchisio and he played in Vucinic, who slotted the ball home to put Juventus closer to a last-eight berth.