Despite not having played a competitive game for two months, the Norwegian outfit took a shock lead when Albert Grønbæk rounded off a spectacular team goal by sliding a low effort into the bottom corner from inside the area, leaving goalkeeper Diant Ramaj glued to his spot.
That silenced a shell-shocked Dutch crowd, who soon saw Fredrik André Bjørkan fire off target from distance as the visitors continued to impress.
John van't Schip’s side started to improve though, creating an opening for Tristan Gooijer, who had a whipped 20-yard effort saved, before Kenneth Taylor and Chuba Akpom fired over from a similar range.
Those two chances came after a huge heart-in-mouth moment at the other end, when a Ramaj pass clattered into Sondre Sørli and was dribbling towards goal before being cleared.
Ajax continued to flounder after half time, with Berghuis curling past the far post as chances were few and far between.
They were then left with a mountain to climb when a fortunate deflection fell Grønbæk’s way in the area, and he confidently tucked the ball into the far corner. That sucked the life out of the hosts, whose faltering campaign looked set to take another miserable turn.
However, there was to be some late drama, as Branco van den Boomen pulled one back from the penalty spot after Brian Brobbey, who had earlier missed a sitter of a header, was hauled down in the area by Odin Bjørtuft, who was subsequently sent off.
And then with just seconds of added time remaining, Bodø/Glimt were broken when Berghuis received possession in the area and dinked the ball over the goalkeeper, who had come off his line and was out of position after flapping at a cross.
The result means the two teams are all-square ahead of the second leg in Norway next week.
Flashscore Man of the Match: Albert Grønbæk (Bodø/Glimt)
See a summary of the match here
