The Austrians, who needed a win to qualify, were by far the better side with Mergim Berisha hitting the post early on as they spurned several opportunities.
Diego Simeone, who welcomed back Luis Suarez into the line-up, saw his side soak up the pressure and score typically from a set-piece with Mario Hermoso glancing in a free-kick for his first goal for the club.
The home side continued to dominate and be wasteful in front of goal in the second period. Reported Arsenal target Dominik Szoboszlai and Rasmus Kristensen both failed to find the target from close range.
Enock Mwepu hit the post in the closing stages with a long-range effort but the Liga leaders sealed victory through Yannick Carrasco’s late volley to book their place in Monday’s draw for the last 16 while Salzburg drop into the Europa League.