The hosts had won their last four home games against Italian opposition, but it was their opponents - two-time winners of the competition - who started brightest. Francisco Conceicao had an early chance, stinging the goalkeeper’s fingertips with a rasping drive from the edge of the box, before Vasilije Adzic lobbed a back post volley onto the roof of the net.
At the other end, Ole Didrik Blomberg came agonisingly close with a strike that bobbled narrowly wide, before he converted his first UCL goal minutes later from just yards after ghosting onto a Kasper Hogh flick on from a corner and firing his side into a 1-0 lead.
That spurred the visitors into life, and Adzic nearly equalised with a strike that was expertly saved, as did Conceição on the stroke of half-time, but only after Patrick Berg had been denied by Mattia Perin and Høgh had seen a deflected shot spin narrowly wide for the Norwegian side.
A big second half lay ahead, and Luciano Spalletti’s side started it perfectly when Lois Openda profited from some penalty area pinball, as possession fortuitously fell his way and he duly lashed a crisp right-footed effort into the back of the net, ending a goal drought that stretched back to early April.
Within minutes, the comeback was complete, as Fabio Miretti - who had just had a goal chalked out for offside - floated an inviting cross to the back post for Weston McKennie, who climbed high to nod home a towering header.
The Old Lady, who were on a run of two wins in 13 outings, were in inspired form by now, and the hosts were struggling to stick with them. Eying a third, Conceicao had a whipped shot tipped around the post, while Perin kept out Berg’s ambitious 30-yard free-kick at the other end.
That sparked a late revival, and Bodø/Glimt were gifted the chance to equalise when Sondre Auklend was clumsily fouled by Juan Cabal, allowing Sondre Fet to hold his nerve and convert from the spot.
There was more drama to come though, as a rapid Juventus counter-attack led to the ball falling to David in the penalty area, and he stroked home a 91st-minute winner that moves his side into the top 24 in the league phase, while they also picked up just their second win from their last 12 away games in the UCL.
Bodo/Glimt meanwhile have a mountain to climb to make the knock-out stages, as they remain winless from five matches (D2, L3).
Flashscore Man of the Match: Francisco Conceicao (Juventus)