Victory extended the Blues’ undefeated streak under new manager Graham Potter to nine games, while being four points ahead of the Austrian champions at the top of Group E.
Something other than Dinamo Zagreb’s win over AC Milan later on Tuesday also guarantees first place in the group for the 2021 European champions.
Chelsea’s brilliant start under Potter has been undermined by their failure to convert their approach play into goals and that was once again the case in a dominant first 45 minutes.
Salzburg hadn’t suffered a defeat in the first four Champions League games of the season, but was grateful to goalkeeper Philipp Kohn for keeping the score low before half-time.
The excellent attack by Mateo Kovacic in the top corner gave Kohn no chance, as he opened the score in the 23rd minute.
But the German stopper won a personal duel with Pierre-Emerick Aubameyang with three stunning saves to reject the former Arsenal captain.
Havertz also had a close range header that was parried by Kohn as Chelsea clicked into an attacking rhythm rarely seen during Potter’s first two months.
The England side looked like they would regret not taking those chances as Salzburg equalized four minutes into the second half when Junior Adamu put Maximilian Wober’s teasing cross behind the Chelsea defence.
However, the visitors reacted immediately as Kohn rushed out to deny Aubameyang one more time before Adamu Jorginho’s header bounced off a corner.
Chelsea finally got the second goal they deserved when Havertz muffled Christian Pulisic’s pass before curling in through the bottom of the bar.
But Potter’s men had to withstand a late attack from Salzburg to hold onto all three points.
The in-form Kepa Arrizabalaga had to fly low to the left to outrun Benjamin Sesko’s attempt.
Kepa is finally starting to live up to his price tag as the world’s most expensive goalkeeper after his move from Athletic Bilbao in 2018.
But the Spaniard was saved by Thiago Silva’s goal line after being knocked into a cross by Strahinja Pavlovic.
Kepa was called up again in the closing stages to save from Dijon Kameri and Amar Dedic, but Chelsea held out to ensure they are in the draw for the last 16 next month.