The Scottish champions led at half-time in Austria through Odsonne Edouard’s goal but the Die Roten responded after the breaking, hitting three goals without reply.
It will be of little consolation to Brendan Rodgers and his team, but Celtic are the latest big name which have been defeated at the Red Bull Arena.
Since the club’s rebranding following the takeover by Red Bull in 2005 Salzburg have defeated Valencia, Shakthar Donetsk, Lazio (twice), Villarreal, Paris Saint-Germain, Ajax, Schalke, Marseille and Real Sociedad.
Salzburg are currently unbeaten in their last 13 home games in Europe. Of the 64 home European ties they have played since 2006 they have lost just 12 in 90 minutes. Such has been their presence in the Europa League they, like Sevilla of Spain, are naturally linked to the competition.
The victory over Celtic reaffirmed their connection with the Europa League, while strengthening some of the records they hold in the tournament.
No team has made more group stage appearances than Salzburg’s eight, while they are second for most qualifications (five) from the group stages.
The club are one of seven who have qualified from the group stages having won all six games, but they are the only team to achieve that feat twice.
With three goals and three points against Celtic they added to their record as the team to have won most points (89) and scored most goals in the group stages (76).
Having won their opening two fixtures - they defeated RB Leipzig in the opening round - they are well placed to add their most group stages first places (four).