Majestic goals from Mateo Kovacic and Kai Havertz were the highlights of an impressive away performance by Chelsea.
The Blues secured their passage into the knockout rounds of the UEFA Champions League and all but assured themselves of top spot in Group E.
It was a competitive and even start to the game at Red Bull Arena, until Kovacic produced a fantastic, first-time effort with his left foot to put the visitors ahead.
Following the opener, Chelsea really grew into the game and had numerous opportunities to extend their slim lead, prior to the half-time interval. Multiple heroics from RB Salzburg keeper, Philipp Kohn, helped the hosts head into the break only one goal down.
Thanks to this, Salzburg were able to level the score, shortly after the restart. Junior Adamu redirected a precise cross from the left side and the hosts regained hope of extending their remarkable 40-match unbeaten home run.
This was until Havertz unleashed a fantastic strike from the edge of the Salzburg box. It seemed like only an effort like that - finding the top corner, off of a touch of the post, would be enough to beat the on-form Kohn.
Chelsea saw out the final stages of the game with relative comfort. They can now only be overtaken by Dinamo Zagreb - who face Milan, later on tonight and travel to Stamford Bridge, on the final matchday.
Story of the Match
Graham Potter continued utilising the depth of his Chelsea squad - he made four changes from their draw against Manchester United. Raheem Sterling and Christian Pulisic were expected to occupy the wing-back roles; Havertz, Kovacic and Conor Gallagher also came into the 11.
There were three changes for the hosts, from their previous UCL fixture. Bernardo, Maximilian Wober and Adamu came into a team featuring seven players aged 21 or below.
A dangerous early header back to the goalkeeper from Bernardo almost gifted Havertz a chance to give Chelsea an early lead. Kohn bravely threw himself at the ball, to avert the danger and earned a nasty knock on the head, courtesy of Havertz's knee, in the process.
Following a few decent early bits of attacking play by Chelsea, Salzburg were able to settle into the game, as the game passed the 10-minute mark.
The hosts were not allowing Chelsea to keep possession with any deal of comfort. Another good bit of Salzburg pressure led to Luka Sucic having an effort at goal - which sailed handsomely over the bar.
For all of the visitors' possession, they were unable to have any efforts at Salzburg's goal - until the 23rd minute.
Kovacic was the man who had that first effort at goal and it resulted in Chelsea taking the lead. A scruffy passage of play in and around the Salzburg box led to the ball bouncing to Kovacic - who was able to produce a guided, first-time finish, with the inside of his left foot. The ball faded into the top corner, beyond Kohn's reach.
Shortly after, a deflected Pierre-Emerick Aubameyang header, from a Chelsea corner, had to be very well stopped by the keeper.
Another opportunity for the forward came at around the half-hour mark. This time, a clear-cut chance, which came from Chelsea expertly playing through the Salzburg press. Aubameyang had plenty of time and space, following Havertz's pass, but he was unable to beat Kohn from close range.
Kohn was a very active figure throughout the first half. After, yet again, a fluid bit of play from Chelsea, the goalkeeper had to be quick off his line to smother the potential danger in the form of an oncoming Aubameyang - getting to the ball just before the forward.
The last action before the break saw Kohn shine, again. He was able to deny Aubameyang for the umpteenth time in the first half. A powerful, low effort was very well kept out, at the keeper's near post.
Following an even start to the match, Chelsea headed into the break in a very deserved 1-0 lead. As the half went on, they only improved more and more and looked to carry that momentum into the second half.
Instead, Salzburg got off to a lightning start, following the interval. Chelsea were put onto the back foot immediately and it took just four minutes for the hosts to earn an equaliser.
Wober's pinpoint ball from the left side allowed the oncoming Adamu to meet the delivery and produce a first-time finish past Kepa. The close distance to the goal and the forward's central position ensured that the keeper had very little hope of keeping the ball out of the net.
Salzburg were rewarded for their fast start to the second half. However, following the equaliser, Chelsea returned to being the more dominant team and were able to, again, exert their earlier dominance.
A positive period of play ensured that The Blues were able to go back ahead, courtesy of a quite special goal, in the 64th minute.
An impressive bit of footwork from Pulisic led to the American finding a pass to Havertz, with the forward in a central position, just outside of the box. Havertz controlled the ball and unleashed a perfect, whipped effort which struck the post before making its' way into the top corner; a truly majestic strike.
For all of the hosts' subsequent attempts at levelling the scoreline, Chelsea defended with great assurance and discipline and did not allow too much danger near Kepa's goal.
Chelsea's best chance, following the Havertz goal, fell to Pulisic - who was unable to make contact with his effort at goal. The ball ran through to Gallagher and his attempt was blocked.
Salzburg late period of pressure featured Kepa being called into action - saving a long-range effort and a strike from Amar Dedic. The Blues were able to hold on for the win and seal their place in the knockout rounds.
Player of the match - Philipp Kohn
The fact that a Chelsea player does not earn the player of the match award does not suggest that their performance did not deserve it going their way.
Instead, it is a credit to Kohn, that his exceptional efforts in the Salzburg goal ensured that the game remained competitive, right until the final whistle.
Kohn was forced into making a total of eight saves - seven of which came from efforts from inside the Salzburg box. A hugely impressive performance, which the Swiss keeper should be immensely proud of.