Alessandro Matri struck early before late goals from Claudio Marchisio and Mirko Vucinic virtually assured the Bianconeri of a place in the next round.
Alessandro Matri opened the scoring with less than three minutes played, and Claudio Marchisio and Mirko Vucinic gave the hosts a steep mountain to climb in the second leg with two late strikes to account for the goals.
Having already beaten Barcelona, the Bhoys went into the game quietly confident of toppling another European giant; however, the hosts were left reeling after less than three minutes of action.
Efe Ambrose, who had only just returned from African Cup of Nations duty with Nigeria on the morning of the game, appeared to be suffering the effects of a long-haul flight when he made a mess of an attempted header back to Fraser Forster. That allowed the in-form Matri to steal in and lift the ball over the advancing keeper for a crucial away goal for the Bianconeri.
The scrambling Kelvin Wilson looked to have pulled off a remarkable last-ditch clearance, but replays showed that the ball had crossed the line. Even if Wilson's clearance had stood, Marchisio had put the issue beyond all doubt by calmly burying the rebound.
The concession of such an early away goal undoubtedly came as a hammer blow for Celtic, but the hosts quickly cleared their heads and set about hammering away at the Juventus goal. Buffon was twice called into action to deal with well-struck drives from Victor Wanyama and Kris Commons, before the latter volleyed over when well placed in the middle of the box.
Juve was struggling to exert its customary control over the middle of the park, with Andrea Pirlo growing increasingly frustrated by the roughhouse treatment he was receiving from Scott Brown, in particular. After becoming embroiled in an unsightly outbreak of handbags, the peerless playmaker began to express himself in a far more positive fashion, prising open the Celtic defense with a sublime throughball. Vucinic managed to get on the end of pass, but the Montenegrin’s first touch forced him too far wide and the chance to double Juve’s lead passed.
The home side did its best to sustain the frenetic pace it had set in the first half, but the Bianconeri stubbornly refused to break. Ambrose had a glorious opportunity to atone for his earlier error on the hour mark but he hit an unmarked header from close range straight at a grateful Buffon.
The visitors, as a consequence, became increasingly adventurous the longer the game wore on and Marchisio doubled Juve's advantage with just more than 15 minutes remaining. The midfielder fired past Forster after turning sharply inside Scott Brown.
The Serie A champions then put the game - and effectively the tie - out of reach when Marchisio slipped Vucinic through to score a third goal with just seven minutes to go, thus killing what little fight Celtic had left in them. The Bhoys must overturn the three-goal deficit in Turin during the return leg or else their Champions League run will come to an end.