Bodo/Glimt embarrassed Celtic at Celtic Park, leaving them with a mountain to climb to reach the last 16.
Runar Espejord gave the Norwegian champion an early lead.
Daizen Maeda brought the tie back to life when he headed in, but Hugo Vetlesen's shot immediately flattened the atmosphere in Glasgow.
It leaves Celtic with a two-goal deficit to overcome in Norway next week.
Celtic had a nine-game winning run that ended with the result.
The Norwegians have yet to start their season, and Celtic went at them early to test their match sharpness.
When Maeda slipped inside his marker and had a sight of goal, he allowed it to run before cutting it back where the defence were able to get it away.
Bodo/Glimt showed what a good team they are after that.
They had their lead after Joe Hart was shot down by Pellegrino.
Espejord got the goal-side of Carl Starfelt after Kjetil Knutsen's side knocked one-touch passes around the Celtic defence. He poked the ball through the gap and into the net.
Even though their own attacking intent waned, they continued to frustrate Celtic. Dominating possession, slowing down the pace of the game, and cutting out every avenue Celtic tried to play through to Maeda.
There were two appeals for penalties, one when Jota was tripped and the other when goalkeeper Nikita Haikin took out Cameron Carter-Vickers.
The game lacked a spark as Bodo/Glimt threatened a second. The crackle of electricity that made this stadium a hive of activity was missing.
The second half began with a bit more movement and verve. Jota blasted over and Maeda's shot was charged down as they passed the ball with purpose and started to work Bodo's backline.
Less than 10 minutes into the second half, the Norwegians were 2-0.
Bodo combined his front three in a smart move. Espejord had the easy task of picking his spot in the back of the net when he saw that Ola Solbakken darted past Greg Taylor, his pass was cutely flicking on by Espejord, and he had the easy task of picking his spot in the back of the
Something to take to Norway was what Celtic needed. Jota found space and had a shot tipped over the bar, as they continued to press, they got their breakthrough to keep the tie alive.
Maeda glanced a Josip Juranovic cross past the goalkeeper.
Within two minutes, the fire was out.
Vetlesen took aim from outside the box and his shot went over Hart.
As the stands emptied, Celtic tried in vain to cut the deficit to one again, but little would fall for them on a frustrating night.
Celtic has built their success on pace and movement. Scottish teams have struggled with it.
Bodo/Glimt got to grips with it quickly. They made Celtic look ordinary by holding on to possession.
The hosts were not terrible. They forced saves, at times passed it well, and it was a slice of misfortune with the third goal which restored the two-goal deficit.
They need to do well in Norway next week to keep their European hopes alive.
It is only half-time, according to the Celtic managers. We will go there and play our football and see what happens.
We got ourselves back into the game. They took a shot from outside the box and it took a deflection. There are things that happen in football. Goals change the context of a football game.
We have to go there and play our football again. It is a good challenge for us to score goals away from home.
Formation 4-2-3-1.
88Juranovic20Carter-Vickers4Starfelt3Taylor11Abada18Rogic17Neves FilipeFormation 4-3-3.
3Sampsted18Moe4Høibråten5Wembangomo10Vetlesen23Hagen14Saltnes9Solbakken28Espejord11PellegrinoThe match ended with Celtic winning 1, Bodø/Glimt 3.
The second half ends with Celtic winning.
An attempt was missed. Carl Starfelt's left footed shot from the centre of the box misses to the left.
Bodø/Glimt. Victor Boniface is caught off guard by a through ball.
The substitution was Bodø/Glimt. Mvuka replaces Solbakken.
The substitution was Bodø/Glimt. Sery replaces Wembangomo.
The attempt was saved. Reo Hatate's shot from the right side of the box is saved in the top right corner. Josip Juranovic assisted.
An attempt was missed. The Celtic player's head is too high from the centre of the box. Daizen Maeda assisted.
Nikita Haikin is shown a yellow card.
The free kick was won in the defensive half.
Foul by Victor Boniface.
James Forrest had a foul.
Konradsen won a free kick in the defensive half.
Corner, Celtic. There was a Conceded by Alfons Sampsted.
Goal! Celtic 1, Bodø/Glimt 3. Hugo Vetlesen shot from outside the box to the high centre of the goal. They were assisted by Ola Solbakken.
Goal! Celtic 1, Bodø/Glimt 2. Daizen Maeda headed from the centre of the box to the bottom left corner. Jo Jursipanovic assisted with a cross.
Bodø/Glimt. Morten Konradsen is caught off guard when he tries a through ball.
The substitution was Bodø/Glimt. Ulrik Saltnes was replaced by Morten Konradsen.
Giorgos Giakoumakis (Celtic) has a foul.
Brede Moe won a free kick in the defensive half.