Reeling from their joint-heaviest UCL defeat in over a decade against Liverpool, Leverkusen came out with intent, storming to a two-goal lead within the opening 15 minutes.
A contentious handball by Samson Baidoo inside the area prompted referee Mikola Balakin to award a penalty, which Florian Wirtz dispatched with precision into the right corner.
Moments later, Alejandro Grimaldo doubled the advantage, curling a sublime free-kick into the top corner, leaving Alexander Schlager rooted between the sticks.
Before long, Pepijn Lijnders’ side crumbled on the half-hour mark.
Wirtz stole the spotlight with a sublime solo effort, taking out a handful of opposition defenders inside the box, before burying the ball into the back of the net.
Leverkusen nearly widened their advantage twice before the break, as Exequiel Palacios fired a close-range effort off target and later saw his header soar over the crossbar.
Despite introducing three fresh faces after the interval, the Red Bulls struggled for inspiration. Leverkusen continued to dominate, determined to extend their impeccable European home record, now unbeaten in seven consecutive outings at the BayArena.
Patrik Schick eventually broke through, expertly meeting Jeremie Frimpong’s pinpoint cross from the right flank to fire a first-time finish into the net from point-blank range.
A swift counterattack then saw Wirtz turn provider, threading a perfect pass for Aleix Garcia, whose powerful strike slipped past Schlager's outstretched arms.
The defeat means Salzburg have now lost three games in a row, after having started their UCL campaign with three defeats ‘to-nil’, despite ending their eight-match winless Champions League run with a victory over Feyenoord last matchday.
The story is different for Xabi Alonso’s Leverkusen though, who remain unbeaten against Austrian opponents in six European meetings. Die Werkself have now scored more than Liverpool and Manchester City since the start of last season in Europe, while also winning more games in major European competition than any other side, excluding qualifiers.
Flashscore Man of the Match: Florian Wirtz (Bayer Leverkusen)