They will also need a miracle in the Juventus Stadium on March 6. The 3-0 defeat suffered in last night's first leg against the Italians has left Neil Lennon's men hurtling towards the end of their European campaign.
The club's two previous sojourns to the last 16 saw them held to a goalless draw at home by AC Milan in 2007, before they lost to a Kaka goal in extra time in the San Siro.
A year later, it was Barcelona who destroyed their quarter-final dream, winning 3-2 in Glasgow before sealing the deal with an early goal in the Nou Camp.
Turning this tie around will be immeasurably tougher, given the margin of Juve's lead and how well they are playing as they lead Serie A in defence of the title they won without suffering a single defeat last season.
This is matched by their European record. Antonio Conte's side arrived in Glasgow buoyed by the fact they were unbeaten in 16 previous European games stretching back to 2010 – including their six group stage games this season.
So, it was essential Celtic got some kind of foothold in the tie ahead of going to Turin in three weeks. This they failed to do, by quite some way.
After performing so well in this Euro run, Lennon understood this was going to be something else again.
He had predicted a war of attrition. At times it was just a plain old, ugly war – which they lost.
The news that wrestling was out of favour and dropped from the Olympics from 2020 clearly had not reached the players as the grappling which took place, especially in the goalmouth as corners were being fired in, confirmed.
Juve are not Italian champions for nothing. They know how to play the game, and how to take the rules to the limit.
They are very well drilled and hit viciously on the break.So, scoring after only three minutes set the night perfectly for Andrea Pirlo and Co.
But what a cheap goal it was to concede. A simple ball played from their own half put Efe Ambrose under pressure.
The Nigerian had been given a vote of confidence by Lennon, despite the fact he had only been back in the country a matter of hours after helping his country win the Africa Cup of Nations in Johannesburg on Sunday.
He caught his flight okay, but failed to catch the flight of this ball, and Alessandro Matri put on the after burners to nip in ahead of the advancing Fraser Forster.
Kelvin Wilson tried to slide in to prevent the ball crossing the line, and hooked it back out to Claudio Marchisio, who rammed it high into the empty net.
But the officials had already decided Matri's shot had crossed the line, and Juve had the away goal Celtic could not afford to concede let alone gift.
The irony is that the Hoops had looked the more likely to take the lead as they flew out of the blocks, with Victor Wanyama and Ambrose firing in decent shots.
Kris Commons and Charlie Mulgrew also tried their luck, and the statistics after half an hour revealed Celtic had put five shots on target, to Juve's one. But that one had given them the advantage.
Their pace of passing was a problem for Celtic, the third runner collecting the ball as the Hoops were still challenging for the first ball.
Possession was hard earned, but easily gifted, and Juve looked more comfortable on the ball.
They did get rattled just before the break when, led by Scott Brown and Gary Hooper, Celtic made the game a bit more physical.
Bookings for the striker – cautioned along with Stephan Lichsteiner for a shoving match at a corner – and James Forrest were the only notes in the ref's book by the break.
Unfortunately, Celtic could not find a way past Gianluigi Buffon, and were caught out trying too hard as Juve hit them with two late sucker punches.
With 13 minutes to go, Marchisio turned Brown in the box and fired a shot which Forster's frame could not keep out.
With seven minutes remaining, any hope of a comeback was completely destroyed as Mirko Vucinic – a handful all night for Ambrose and Kelvin Wilson – dispossessed the Nigerian and got his rewards for a decent shift by knocking home No.3 for Juve.
Celtic's defence had been exposed too often, and the gamble of playing Ambrose had backfired with his part in the first and third goals.
He passed up a glorious chance to atone midway through the second half when he got on the end of a Mulgrew cross eight yards out, but weakly headed into the ground for Buffon to collect.
However, the defender was not alone in finding the going tough. Harsh lessons were delivered to men in Hoops all over the park
With Georgios Samaras unable to play any part, the important extra dimension the Greek has brought to Celtic's European campaign this season was badly missed.
Even if he is fit to play in Turin, it looks like the last European tie of the season has been staged at Celtic Park.