It was a lively first half that could've seen either side in the lead at the break, but it was Liverpool that emerged victorious. Naby Keita gave the Reds the lead after 57 minutes, closely followed by an unbelievable finish from Mohamed Salah only a minute later.
It proved to be a season defining two minutes for the Merseyside club.
Story of the game
Salzburg looked to put Liverpool under pressure right from the kick off, with Erling Håland attempting to run through on goal before Virgil Van Dijk used his pace to snuff out the danger.
Seconds later the defender was called into action once again to deny Hwang, marking a nervy opening few minutes for Jurgen Klopp's side. Indeed, the hosts had a third attempt shortly after courtesy of a long range effort from Enock Mwepu, but it was comfortably held by Alisson.
Liverpool's first chance of the game came from Salah, who took a touch before unleashing a shot straight at Cican Stanković after Dejan Lovren's ball over the top. At the other end, Alisson continued to be very busy, pulling off a good reaction save after seven minutes when Hwang and Takumi Minamino combined.
Moments later Mane had time and space on the edge of the box and drilled an effort inches wide. It could've been 2-2 before 10 minutes.
Just after the 20 minutes mark Hwang nearly played in Håland but Alisson was down to gather it before the forward was able to tap Salzburg in front.
Three minutes later Salah and Mane combined on the break but Mane couldn't get the ball under control and his heavy touch allowed the Salzburg keeper to gather.
Straight up the other end of the pitch, Håland stayed onside to get a shot on target, but Alisson made yet another save. It was a moment of panic for Liverpool as Salzburg cut through the the defence, but the Premier League side managed to survive before Andy Robertson's crucial tackle stifled another attack moments before half time.
At the other end, Liverpool scuffed another fantastic opportunity to break the docklock when Keita put it on a plate for Salah, who dragged his effort wide.
Minamino rolled a shot the wrong side of the post after Håland played him through, breaking from the Liverpool defence. The offside flag eventually went up on the 19-year-old, but replays showed it was extremely tight.
Liverpool turn on the style in second half to secure Champions League passage
Liverpool began the second half in a strong manner, creating a chance early on as Mane chipped a great ball through to Salah, who blazed it over the bar. Heroics from Stankovic then denied Liverpool a certain goal on 50 minutes.
Salah was 1v1 after a good break from the European Champions, but he was unable to take it away from the goalkeeper who got a firm hand on it.
Klopp was forced into an early chance just after the 50 minute mark as Dejan Lovren went to the floor, Gomez replaced the defender.
57 minutes into the contest, Liverpool finally got their crucial lead courtesy of Keita's header. Mane found himself in space down the left-hand side, making his way into the box before chipping a fantastic cross to the midfielder, who was waiting on the penalty spot to steer home.
The Reds kicked on from there, carving chances galore through Mohamed Salah, who squandered plenty of opportunities to double the lead before an incredible goal saw him convert from a seemingly impossible angle.
Just a minute on from Keita's header, the Egyptian picked up a long ball, taking it around Stankovic before using his right foot to find the far corner.
Salzburg, startled, had to play their way back into a game that had somehow slipped away from them in the space of two minutes.
It took 15 minutes, but they created a huge chance with Minamino on 73 - Robertson was there to make a crucial block.
They took off their biggest goal threat shortly after as Håland was replaced by Masaya Okugawa. The Europa League beckoned for the Austrian side. However, it was Liverpool that looked the likeliest of scoring as the clock edged closer to 90 minutes.
With two minutes left to play, the Reds looked to counter but Salah had to avoid touching the ball as he looked offside in the build up. Mane took on the chance that saw his shot deflected over the bar.
Takeaways from the match
Salah doesn't score sitters, he scores screamers
Football, ey? Liverpool fans would have surely been fuming with the forward at half time after he scuffed a number of fantastic chances.
The Reds could've been two or three goals to the good had Salah took them. They were of course, goals he's expected to score.
But just a minute after Keita put them ahead with a pin-point header, Salah was clean through.
He took it round Stanković, though the chance looked to have passed as the angle appeared impossible.
But not for Salah. On his right foot he somehow squeezed it into the far corner to extend Liverpool's lead.
Salzburg favourites for Europa League?
Of course there are some fantastic teams in the competition but this side are more than capable of making a statement.
The hosts caused Liverpool all sorts of problems across the ninety minutes and they were simply undone by 100 seconds of sheer quality from their opponents.
Håland has the potential to become a player of the highest calibre and so long as he remains at the club beyond January, he is more than capable of driving them into the latter stages of the tournament.
Naby Keita has arrived
With the injury to Fabinho a couple of weeks ago, it was more than expected that one of Keita and Oxlade-Chamberlain would come into the fold - as highlighted in a previous article.
That's two goals in two games now for the Reds' no.8, after his goal at the weekend against Bournemouth.
It's not just putting the ball in the back of the net that impresses about Naby's game, though, his skill, drive and all round quality shines on the pitch and he's finally coming into his own.
Injuries will hopefully be behind the 24-year-old as he looks to establish himself as a starter in this Liverpool side.