Goals early in each half from Runar Espejord and Amahl Pellegrino put the visitors in command and Celtic conceded again two minutes after Daizen Maeda had given them a 79th-minute lifeline in the Europa Conference League knockout round play-off.
Hugo Vetlesen's deflected effort gives Celtic a mountain to climb when they head to the Arctic Circle next week.
The visitors had not played a competitive game since December 12, as their domestic season does not begin again until April, and had lost players to the likes of Krasnodar, Lens, Hertha Berlin and Schalke since clinching their second consecutive Norwegian title.
However, they made a flying start and Joe Hart had already made saves before Espejord, a new signing from Heerenveen, slotted home inside seven minutes after some sharp passing around the edge of the Celtic box. Carl Starfelt could not get close enough to make the challenge as the forward netted from 12 yards.
The visitors doubled their lead in the 55th minute following some poor Celtic defending. Ola Solbakken skinned Greg Taylor and delivered a low cross. Espejord's flick left Josip Juranovic out of position and Pellegrino had time to stab past Hart from six yards.
Abada soon headed over from a good chance and Jota forced an acrobatic save but the visitors showed another side to their game with an organised defensive shape.
Celtic Park erupted with hope when Maeda headed home Juranovic's near-post cross but the visitors regrouped with a post-goal huddle and soon restored their two-goal cushion when Vetlesen's 25-yard strike hit off McGregor and looped over Hart.
Earlier in the evening, Rangers earned a stunning 4-2 Europa League knockout round play-off first-leg win over Borussia Dortmund.
In an incredible encounter in the Westfalenstadion, Gers captain James Tavernier scored a VAR-awarded penalty for handball in the 38th minute before striker Alfredo Morelos knocked in the second three minutes later.
There were only 10,000 fans inside the ground due to local Covid-19 restrictions and the 9,500 home supporters could barely believe what they were witnessing.
Light Blues midfielder John Lundstram guided in a third after 49 minutes, only for England's teenage international Jude Bellingham to pull a goal back for the German giants a minute later.
Morelos' drive from 12 yards was helped in by home defender Dan-Axel Zagadou - who conceded the penalty - to stretch the Scottish champions' lead again before Raphael Guerreiro's 82nd counter made it 4-2 which leaves Giovanni Van Bronckhorst's men with the advantage going into the return game at Ibrox next Thursday.