Salzburg scored two goals in as many minutes just before the half-time break through Patson Daka and Takumi Minamino to give the visitors a comfortable lead.
Hwang Hee-chan then added a third in the 69th minute before teenage sensation Erling Haaland grabbed the fourth as Mbwana Samatta scored a consolation goal five minutes from time.
Haaland took his tally to eight goals for this season's Champions League campaign and became the first teenager in the history of the European Cup/UEFA Champions League to score in five consecutive appearances in the competition.
Salzburg moved to three points behind Group E leaders Liverpool and must win against Liverpool in their final group fixture to qualify for the last 16.