Barry Lewtas’ side went into Tuesday’s Group E finale at Untersberg Arena knowing a point would be enough to seal top spot in the pool.
However, they appeared destined for a second-placed finish and a play-off tie as goals from Luka Sucic and Tobias Anselm put Salzburg, who would have won the group with a victory, in command at half-time.
But an impressive, spirited fightback after the break was richly rewarded. Harvey Elliott pulled one back with a 67th-minute penalty, before Tom Hill’s inventive, looping header drew the young Reds level.
And late, late drama was to follow, as Bearne slid home Layton Stewart’s unselfish cut-back with the final kick of the match.
The quality provided by Elliott was evident amid a purposeful start from Liverpool, the 16-year-old wriggling free down the right and digging out a teasing cross inside the opening 30 seconds.
Salzburg goalkeeper Daniel Antosch gathered that delivery on the stretch and then saved a shot from Elliott, who bought space with a neat nutmeg before playing a one-two with Luis Longstaff.
Antosch’s reflexes were tested again soon after. Hill deceived his marker with a superb turn and powered a goal-bound effort towards the far corner, but Salzburg’s captain acrobatically tipped wide.
After enjoying near-total domination in the early stages, the young Reds were served a warning of the hosts’ threat on the counter when Karim Adeyemi burst free and shot, with Ben Winterbottom denying the forward.
And, 11 minutes in, they were undone by a long ball from the back, which Sucic raced onto prior to clipping home the opener.
Leighton Clarkson drilled a first-time strike wide from Hill’s lay-off as Liverpool sought a quick reply, but their difficulties were to worsen midway through the half.
Again, a ball from deep caused problems, with the pacy Adeyemi getting on the end of the pass this time. His attempt was well stopped by Winterbottom, but Anselm was on hand to convert the rebound.
Neco Williams, captaining Liverpool with Curtis Jones part of the first-team squad, strode forward and saw a shot deflect into the side-netting, although it was Salzburg who continued to carry the greater threat.
Only a fine save from Winterbottom, who palmed Peter Pokorny’s low effort wide, prevented the home team from extending their advantage before the break.
Elliott saw strong appeals for a penalty dismissed after he’d brought Clarkson’s lofted pass under his spell and shaped to shoot, only for a defender to apparently impede him.
However, Liverpool were awarded a spot-kick when Antosch was penalised for dangerous play as he punched a cross clear while colliding with Elijah Dixon-Bonner.
Elliott did the rest, the forward coolly slotting in from 12 yards.
Salzburg went so close to restoring their two-goal cushion immediately, Pokorny rattling the top of the crossbar with a controlled, first-time strike once he’d been found free on the edge of the area from a corner.
And that moment was to prove pivotal.
First, Hill rounded off a fine Liverpool move in style, deftly glancing Clarkson's cross in off the bar with 11 minutes remaining before tireless work from Stewart, who seized possession from a defender and set up Bearne, completed a remarkable comeback.
Liverpool U19s: Winterbottom, Williams, Hoever, Van den Berg, Norris (Boyes, 89), Clarkson, Dixon-Bonner (Stewart, 74), Cain (Clayton, 89), Longstaff (Bearne, 80), Elliott, Hill.
Unused substitutes: Davies, Savage, O’Rourke.