Celtic secured Champions League qualification with a Young Boys own goal on a night filled with disallowed goals, missed penalties and red card drama at Parkhead.
The Hoops knew a win at the bottom of the table would guarantee a play-off place, and Kyogo thought he had given them a dream start only to have his goal ruled out for offside.
A Callum McGregor error denied the Japanese striker another goal before a third goal was disallowed, again for offside, as they dominated a side who are yet to pick up a point in the Champions League this season.
Kasper Schmeichel produced a brilliant double save
Luck was not on Celtic's side as Arne Engels' poor penalty was easily saved after Greg Taylor was brought down in the box just before half-time.
Auston Trusty hit the crossbar before Kasper Schmeichel made a brilliant double save to deny Young Boys, but their fortunes changed when Loris Benito accidentally turned Adam Idah's ball into his own net to spark wild celebrations.
Celtic's Daizen Maeda was sent off for a pointless late challenge as they progressed to the knockout stages with a game to spare.
Hoops ends a 12-year wait
Ida celebrates full time
A draw would have left Celtic in need of a result at Villa Park next Wednesday, but the late goal pushed them to 18th place, equal on 12 points with Juventus, Real Madrid, Bayern Munich and Borussia Dortmund.
A win in Birmingham next week would likely see Celtic secure one of the seeded places in the play-off round, if not a top-eight finish and direct entry into the round of 16.
And the late slice of fortune was nothing less than Celtic deserved after a spirited 60-minute performance. Midfielders Callum McGregor, Ingles and Hatati controlled the play and Celtic found space through the visiting back four from the start.
Maeda and Nicholas Cone were roaming the outside regularly but deliveries weren't quite falling flat for Furuhashi.
The Japanese striker's first goal came from offside inside six minutes following a pass from Ingles and Khun quickly moved in behind after McGregor's pass but saw his shot deflect wide after getting past three men.
Kyogo Furuhashi shot into the net, but his goal was ruled out for offside
Hatate and Furuhashi fired wide from half-chances before Kasper Schmeichel made his only effort of the first half to beat out Joel Montero's shot from 25 yards.
Furuhashi then had two goals disallowed in the space of two minutes just after the half-hour mark. The first goal was initially awarded after McGregor robbed Niasse and set up the centre-forward to foul the goalkeeper, but Norwegian referee Rohit Sagi penalized the Celtic captain for a foul after a VAR review.
Furuhashi thought he had given Celtic an early lead
Furuhashi was then flagged for offside again after converting Maeda's cross from close range.
Engels' weak penalty kick in the 41st minute was saved after Taylor's shirt was pulled, but the Belgian saved the mistake to create several chances from set-pieces before half-time. Furuhashi and Hatate came close – twice – to do so.
Arne Engels looks sad about missing a penalty in the first half
The pressure continued after the break. Engels, Maida and McGregor all blocked shots and Trusty headed against the crossbar before Celtic were dealt a powerful punch only for Schmeichel to pull off a brilliant double stop from Darian Mals.
Celtic's energy levels began to decline and Brendan Rodgers made some changes in an attempt to regain momentum, with Alex Valle and Paulo Bernardo coming on midway through the first half before Iida replaced Furuhashi.
There was no immediate impact and the visitors threatened from some set-pieces but Idah's run in behind led to the goal and Schmeichel saved Sandro Lauber's effort in the final seconds of stoppage time.
“A little history”
Celtic boss Brendan Rodgers:
“We didn't score the penalty and that can shake you, but it never does.
“The winning goal was to show that level of composure in the 85th minute of the game, building the game from the goalkeeper straight through the team, up the pitch and then an absolutely amazing pass from Rio.
“We had a bit of luck with the winning goal that we didn't get in the first half.
“I've been in a lot of games here where you end up drawing that game and it's a bit flat at the end, and what's worse is losing a game when you weren't supposed to.
“For us, to win it, I think it shows maturity and shows the growth of this team.
“A bit of history has been made, we haven't been to the knockout stages for a long time.
“If we look at the progress, we've won three games, drawn three, and lost one. Over the course of the Champions League, the consistency has been really good.”
“Big slice of luck, who cares!”
Idah (left) celebrates after his shot rebounded into the net to secure Champions League qualification
former Celtic Defender Mark Wilson on Sky Sports News:
“They definitely deserved it for the balance of play and the chances they created. All three of the goals they scored were correctly disallowed, but you could see they were coming and suddenly the game changed and it looked like they missed it.” .
“The coach makes changes at the right time and Adam Idah, who has had a difficult time, is the one who leads the attack well and takes advantage of the opportunity. It was a lot of luck to score the goal but who cares?”
“There have been many nights at Celtic Park that have gone the other way and Celtic have been knocked out of this tournament, so I don't think Brendan Rodgers will care too much about his side losing control in the second half, just that they had a chance.” “The important goal is the one that will take them to the play-off.”
