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Trailing 3-0 from a disastrous first leg at Celtic Park last month, the Scottish champions were left needing a "minor miracle", in the words of manager Neil Lennon, if they were to cause a huge upset at Juventus Stadium.
But despite a positive Celtic performance and several clear-cut chances in the opening half, the Hoops never posed a real threat to the Italian champions, who will now relish a first appearance in the last eight since their exit to Arsenal in 2006.
With Juventus keeping a clean sheet in their past five Champions League games at home, it was no surprise Lennon called the stadium a "fortress".
"The difference is the quality in the final third," said the Celtic coach.
"We had good chances again and we didn't take them. We played some decent football but we missed some really good chances to score or at least get back into the game.
"Quality counts, and that's what makes the differece between the two teams."
Despite the gulf in budget between the sides, Juve coach Antonio Conte said he had not underestimated Celtic's potential.
"You can't forget Celtic qualified from their group with 10 points, they beat some big teams like Spartak Moscow, Barcelona and Benfica so we shouldn't underestimate them," said the Italian.
"Celtic have a great team and we had to be careful tonight. But now we've achieved the dream of making the quarters. For me, it is my first time as a coach and it is the same for many of my players."
After a nervous start, Juve showed the first threatening signs on 13 minutes when Celtic 'keeper Fraser Forster was forced out to block as Fabio Quagliarella threatened to pounce on midfielder Paul Pogba's superb through ball.
Celtic were pressing high up the park and forcing Juve to defend in numbers, however the visitors were often found wanting in a midfield marshalled by 19-year-old Pogba and veteran Andrea Pirlo.
Celtic's first real chance came on 22 minutes when Kris Commons found Joe Ledley in space but the midfielder's shot was wide.
Two minutes later, Federico Peluso robbed striker Gary Hooper and fed Quagliarella to the left of goal. When Forster failed to hold the Italian's shot, Matri ran in to sweep the ball home.
Celtic regrouped and minutes later, Juve were indebted to Gianluigi Buffon's reflexes after the 'keeper dived to palm away a Commons shot which had deflected off Hooper's boot.
At the other end, Arturo Vidal wasted a great chance to double Juve's lead, striking Quagliarella's crossfield ball first-time when he had time to control and shoot.
Celtic were pouring forward at every possible opportunity but Hooper missed the chance of the match for the visitors when he failed to toe-poke Samaras' shot across goal past a beaten Buffon.
Lennon replaced right-back Adam Matthews with Efe Ambrose -- blamed as the culprit for two of Juve's first leg goals -- at half-time, but it was Juve who moved up a gear.
On 49 minutes, Celtic's defence was static when a Pogba through ball to Matri was laid off for Quagliarella, whose shot was well saved by Forster.
Juve were finally starting to play and only a timely intervention from centre-back Kelvin Wilson stopped Quagliarella and Matri combining for the hosts' second goal.
At the other end, Samaras' probing header from the back post back into the area found no takers and then an Ambrose header from a corner went over the bar.
When Juve's second goal came, it exposed Celtic's defence all too easily.
A long ball from midfield was flighted in for Vidal who sneaked in behind Emilio Izaguirre to collect and square for the unmarked Quagliarella to slot home past Forster at the back post.
If Celtic's heads went down, they didn't show it, but the likelihood of piercing Juve's impenetrable backline did not increase as the match wore on.
In a rare slip, Pogba lost possession to Commons on 72 minutes but the forward's strike was blocked.
Seven minutes from time, Samaras had time and space to pick his spot after Ledley's lay-off, but the Greek sent a rising shot over bar.
Juve almost made it 3-0 in the final minutes only for Quagliarella to send a spectacular bicycle kick shot just wide of Forster's upright.