The hosts looked as though they could be on the end of the type of Champions League comeback they had become famous for in what was their first home game in the competition since arguably the greatest of the lot - their 4-0 semi-final win over Barcelona en route to the trophy last season.
The holders raced into a 3-0 lead within 36 minutes and looked to be cruising to a first win of the campaign following their defeat to Napoli on matchday one, only for Salzburg to demonstrate their attacking prowess as they came roaring back.
Hwang Hee-chan sparked the comeback with a goal shortly before half time, and further strikes from Takumi Minamino and substitute Erling Braut Haaland completed a famous comeback for the visitors - a mini 'IstanRedBull'.
The miraculous recovery ultimately proved to be in vain as Mohamed Salah's second of the night ensured a seven-goal thriller ended in Liverpool's favour, but Salzburg once again showed that they can be a force in Group E.
Salzburg arrived at Anfield with a fearsome attacking reputation having scored six goals on matchday one and 55 goals in 12 games across all competitions this season, but their chief marksman Haaland - linked with a host of Europe's top clubs following his hat-trick against Genk - was only deemed fit enough for the bench due to illness.
The visitors still had the first sight of goal of the night, with Minamino finding space outside the area within three minutes and drilling a low strike wide of the target.
Liverpool soon gained control of the contest, though, and there were a couple of bright attacking moments before Mane opened the scoring in the ninth minute with a fine goal, exchanging passes with Roberto Firmino before sliding his finish beyond the keeper.
The Senegal international refused to celebrate against his former club, but there was no such reticence from Liverpool's two full-backs when they combined for a second midway through the first half.
Robertson made a driving run forward to spark the attack and continued on into the box after releasing the ball, eventually showing all the instincts of a centre-forward to get to the near post and steer Trent Alexander-Arnold's low cross home from close range.
It should have been three on the half-hour mark when Fabinho clipped a pass over the top for Salah to race on to, but the Egyptian winger lashed his half-volleyed finish wide of the target with the keeper stranded.
There was a warning shot from Salzburg moments later when Dominik Szoboszlai poked the ball through for Minamino, who was denied by Adrian, but it appeared to be game over when Liverpool made it 3-0 five minutes later.
Salah's first of the night was a much scrappier goal than the two which preceded it, with Firmino's glancing header from Mane's cross parried straight back out into danger by Cican Stankovic, leaving Salah with a simple finish.
At that stage it looked like it would be a case of how many Liverpool would get, but Salzburg began their incredible fightback just three minutes later when Hwang collected the ball inside the area before beating Virgil van Dijk all ends up and thumping a clinical finish into the far corner.
Even with that setback late in the first half, few could have predicted how a madcap second half would pan out, although Salzburg did offer signs of what they were capable of - warnings which Liverpool failed to heed.
Another arrived eight minutes into the second half when a slick team move ended with the ball being dropped back to Hwang on the edge of the box, but this time the Korean's strike was not clean as he dragged it comfortably wide.
A frantic end-to-end period ensued with Georginio Wijnaldum and Mane both threatening to restore Liverpool's three-goal lead either side of Szoboszlai only being denied by a crucial last-ditch challenge from Joe Gomez.
Salzburg did get a second moments later, however, with Hwang swinging a fine cross in for Minamino, who met it with a difficult first-time volley which left Adrian no chance.
With the momentum suddenly fully in Salzburg's favour they continued to pour forward and should have levelled things up shortly before the hour mark when Hwang again pulled the strings to tee up Szoboszlai, who took too long over his finish and could only find the side-netting.
Jesse Marsch's men would not have to wait long for that famous moment, though, with Haaland netting just two minutes after coming off the bench with a simple tap-in from Minamino's cross - perhaps the easiest of the striker's 18 goals from just 11 games this season.
It was an almost inconceivable comeback considering the gulf in class there seemed to be during the opening 36 minutes, but once they got level Salzburg appeared to take their foot off the pedal - something which allowed a reeling Liverpool to regain a foothold in a game they had completely lost control of.
The introductions of James Milner and Divock Origi in the immediate aftermath of the equaliser helped in that regard too, and Liverpool's blushes were spared 21 minutes from time when Salah restored their lead.
Salzburg failed to properly clear their lines, allowing Fabinho to hoist the ball back into the area and Firmino to glance it on for Salah, who finished with aplomb.
Anfield breathed a collective sigh of relief but would have been eager for another two-goal cushion having seen what had already happened on the night, and they almost got their wishes in scenes reminiscent of the goal which took them to the final at Barcelona's expense last season.
Much like the quick corner which caught out the Spanish outfit, Alexander-Arnold fired a low cross in to the near post which Mane looked certain to nod home from close range, only for the attacker to misjudge the ball and fail to make any contact whatsoever.
Salzburg sub Masaya Okugawa fired another reminder - as if Liverpool needed one - of Salzburg's constant attacking threat when he drew a routine stop from Adrian, but that proved to be the final major scare for the hosts as they saw the game out in the final 10 minutes.
The win sees Liverpool move onto three points in Group E, one behind leaders Napoli after they were held to a goalless draw by Genk and level with a Salzburg side they may not relish playing away from home after this experience.
LIVERPOOL (4-3-3): Adrian; Alexander-Arnold, Gomez, Van Dijk, Robertson; Henderson (Milner 62'), Fabinho, Wijnaldum (Origi 64'); Salah (Keita 91'), Firmino, Mane
RED BULL SALZBURG (4-4-2): Stankovic; Kristensen, Onguene, Wober, Ulmer; Minamino, Mwepu, Junuzovic (Ashimeru 78'), Szoboszlai (Okugawa 71'); Daka (Haaland 56'), Hwang