Although Mateo Kovacic's first-half strike was cancelled out by Junior Adamu, Kai Havertz netted one of the best goals of his Chelsea career to secure a spot in the last 16 for his club with a game to spare.
In producing arguably their best performance since the arrival of Graham Potter, the Premier League giants also ended Red Bull Salzburg's 40-match unbeaten record in all competitions.
Chelsea now sit six points clear of Dinamo Zagreb and AC Milan, who square off in Croatia later on Tuesday evening.
Potter made the decision to tinker with his Chelsea XI, using Christian Pulisic and Raheem Sterling as wing-backs while also deploying a central-midfield three.
During the opening quarter-of-an-hour, it remained questionable whether the change of strategy would pay off as Salzburg matched their more illustrious opponents, but Chelsea began a spell of first-half dominance with an outstanding finish from Kovacic.
While the ball was diverted into his path by a Salzburg defender, the Austrian-born midfielder scored just his fifth goal in 197 appearances for Chelsea with a wonderfully-instinctive effort with his left foot which found the top corner from 16 yards out.
Chelsea then proceeded to showcase their most attractive football since Potter's arrival, Pierre-Emerick Aubameyang initially seeing a header saved from a corner before he failed to cap off a sensational team move by firing too close to goalkeeper Philipp Kohn.
Havertz was the next to go close, directing a tame header straight at Kohn when he should have scored, before the Salzburg stopper pulled off a brilliant stop to deny Aubameyang from 15 yards just before the half-time whistle.
Potter would have been concerned that Chelsea's lack of a ruthless streak would come back to haunt them, and it did just three minutes after the restart as Salzburg netted a tremendous goal on the counter.
After Maximilian Wober got down the left flank, he proceeded to whip a pinpoint cross into the path of Junior Adamu who coolly slotted a first-time effort past the advancing Kepa Arrizabalaga.
Chelsea responded immediately, almost going ahead on two occasions with Aubameyang again being denied by Kohn before Jorginho saw a header cleared off the line.
However, Chelsea got their noses in front for a second time courtesy of a moment of brilliance from Havertz, the German turning on the edge of the box before curling a shot into the top corner of the net via the underside of the crossbar.
Although the home side were momentarily stunned, they soon got back on the front foot with Benjamin Sesko forcing Arrizabalaga into a sharp stop low down to his left.
Arrizabalaga almost went from hero to zero, mistiming a punch on the penalty spot to allow Strahinja Pavlovic's header to bounce towards goal, but Thiago Silva was able to clear off the line.
While Chelsea threatened a third goal on the odd occasion, Salzburg had the better of the closing 15 minutes, resulting in some increasingly-frantic defending from the Blues backline.
Nevertheless, Arrizabalaga was not called upon to make a better save than he had already done so from Sesko, helped by commanding performances from each of Trevoh Chalobah and Silva.
Potter's unbeaten streak as Chelsea boss has now been stretched to nine matches, and he will now prepare to return to the Amex Stadium to face former club Brighton & Hove Albion on Saturday afternoon.