Celtic secured Champions League promotion with a Young Boys own goal in a night of disallowed goals, missed penalties and red card drama at Parkhead.
The Hoops knew a win against the bottom-table side would all but guarantee a place in the play-offs and Kyogo thought he had given them the dream start only to have his shot ruled out for offside.
Callum McGregor's foul saw the Japanese striker denied again before a third goal was ruled out, again for offside, as they dominated against a side yet to pick up a point in this season's Champions League.
Kasper Schmeichel made a great double save
Luck was not on Celtic's side with a poor penalty easily saved by Arne Engels after Greg Taylor was brought down in the box before half-time.
Auston Trusty hit the bar before Kasper Schmeichel pulled off a superb double save to deny the Young Boys, but their fortunes turned when Loris Benito turned Adam Idaho's ball into his own net to spark wild celebrations.
Celtic had Daizen Maeda sent off for a late, pointless challenge as they progressed to the knockout stages with a game in hand.
The hoops end a 12-year wait
Adam Idah celebrates full time
A draw would have left Celtic with a potentially much-needed result at Villa Park next Wednesday, but a late goal left them in 18th place, level on 12 points with Juventus, Real Madrid, Bayern Munich and Borussia Dortmund.
A win in Birmingham next week would likely see Celtic clinch one of the seeds in the play-off round, if not a top-eight finish and a direct place in the last eight.
The late bit of luck was no less than Celtic deserved for a performance that was full of fervor throughout 60 minutes. Midfielders Callum McGregor, Engels and Hatate dominated the game, and Celtic found space through the visiting back four from the start.
Maeda and Nicolas Kuhn were passing outside regularly, but the deliveries weren't really falling to Furuhashi.
The Japan striker's first offside came after six minutes from Engels' pass, and Kuhn soon got in behind after McGregor's pass, but his shot deflected high after going past three players.
Kyogo Furuhashi shot at the net, but his shot was ruled out for offside
Hatate and Furuhashi shot wide at half-chances before Kasper Schmeichel made his only stop of the first half, beating Joel Monteiro from 25 yards.
Furuhashi then had two goals scored within two minutes just after the half hour mark. The first was initially awarded after McGregor robbed Niasse and set up the centre-forward to mis-hit the keeper, but Norwegian referee Rohit Saggi booked the Celtic captain for the foul following a VAR review.
Furuhashi thought he had given Celtic an early lead
Furuhashi was then ruled offside again after converting Maeda's cross from close range.
Engels had a weak penalty saved in the 41st minute after pulling Taylor's shirt, but the Belgian shook off the miss and created several chances from set pieces before the break. Furuhashi and Hatate – twice – came close.
Arne Engels looks dejected after missing a penalty in the first half
The pressure continued after the interval. Engels, Maeda and McGregor had shots saved and Trusty headed against the crossbar before Celtic were almost hit with a powerful strike only for Schmeichel to pull off a brilliant double stop from Darian Males.
Celtic's energy level began to wane and Brendan Rodgers made some changes in an attempt to regain some impetus, Alex Valle and Paulo Bernardo came on midway through the half before Idah replaced Furuhashi.
There was no immediate impact and the visitors threatened in some set pieces, but Idaho's run from behind led to a goal and Schmeichel saved Sandro Lauper in the dying seconds of stoppage time.
'A bit of history'
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Celtic manager Brendan Rodgers says the players showed “maturity and development” in a 1-0 win against Young Boys to secure a place in the Champions League play-offs.
Celtic the manager Brendan Rodgers:
“We didn't score a penalty and that can shake you, but it never did.”
“The winning goal, to show that level of composure in the 85th minute of the game, to play from the 'keeper on the way through the team, to the side of the field and then an absolutely incredible pass by Reo.
“We got that bit of luck for the winning goal that we never had in the first half.
“I've been in a lot of games here where you end up pulling that game out and it ends up being a bit flat, and even worse you lose the game when you shouldn't have.
“For us to win that, I think it shows the maturity and development of this team.
“A little bit of history was created, we were not in the knockout phase for a long time.
“If we look at the progress, we've won three games, we've drawn three games, we've lost one. During the Champions League, that's really good consistency.”
'A huge piece of luck, who cares!'
Idaho (L) celebrates after his shot deflected into the net to secure Champions League promotion
Ex Celtic defender Mark Wilson he Sky Sports News:
“They certainly deserved it with the balance of the game and the chances they created. The three goals they scored were properly disallowed but you could see it coming and suddenly the game just changed and it looked like they blew it.
“The manager is making changes at the right time and Adam Idah, who is having a rough old time, is actually leading the line well and taking advantage of the opportunity. A huge piece of luck to score but who cares?
“There have been many nights at Celtic Park that have gone the other way and Celtic have crashed out of this tournament, so I don't think Brendan Rodgers will care too much that his side lost control in the second period, as long as they got the goal that mattered and that's the one that takes them to the play-offs.”