Brendan Rodgers was taking charge of the club for the first time in a competitive match, but it turned out to be one of the lowest moments in their history as they fell to an infamous defeat in the first leg of their Champions League second qualifying round tie.
Celtic, as expected, dominated possession in the early stages of the match, but they struggled to get any sort of fluency going in their attack as the hosts dealt with everything that their more illustrious opponents could offer.
Indeed, it was the part-timers who had the first shot on target of the match after half an hour when Liam Walker skipped away from Kieran Tierney in the area before going for goal, but Craig Gordon was equal to the effort.
Celtic did have the ball in the back of the net moments later when new signing Moussa Dembele climbed highest in the penalty area to nod home, but the referee cut the celebrations short by awarding a free kick for a foul on the keeper.
Tom Rogic had a rare shot on target for the visitors that was comfortably gathered by the keeper before Celtic finally had their first real chance of the match when Dembele took the ball down, created space to shoot and drew a low stop from 38-year-old Raul Navas.
Rodgers's first 45 minutes as Celtic boss ended goalless, though, and things soon got even worse when the Red Imps took a shock lead just three minutes after the restart.
Efe Ambrose had put in an unconvincing first-half showing, and he was once again at fault for the opener as he failed to cut out a pass to Lee Casciaro, who turned away from the Celtic defender before poking his finish past Gordon.
The same player - a part-time policeman - had also scored past the Scottish national team for Gibraltar, writing his name into the history books with his country's first ever competitive goal.
One very nearly became two moments later as Lincoln began to take the game to the Scottish champions, with Calderon Vallejo powering into the box before cutting inside and curling an effort narrowly over the crossbar.
It continued to be the home side who looked most like scoring, with Gordon again called into action to keep Patino Blasco's long-range strike out shortly before the hour mark.
Celtic responded immediately this time, though, coming within inches of levelling things up when Leigh Griffiths's shot from inside the area deflected against the crossbar.
The visitors, who were crowned champions of Europe in 1967, continued to look for a goal that would spare their blushes, but Stuart Armstrong blazed another chance over the crossbar with 20 minutes remaining after he combined with James Forrest.
Rodgers would have been beginning to think that it wasn't his day when Celtic hit the woodwork for a second time in the 78th minute, though, and again it came from Griffiths as the striker's free kick struck the bar before Nir Bitton failed to turn the rebound goalwards.
Substitute Nadir Ciftci was the next to go close for the Bhoys, but there was still no way through as Navas parried the striker's header away from goal in the closing stages.
Ciftci had one more chance at the death which he could only head over as Lincoln Red Imps held on for the most famous result in their history, while Rodgers's reign got off to the worst possible start.