The defeat was the latest blow to the Austrian champions whose dreams of playing in the Champions League have been shattered once again and who began their Europa League campaign with a 2-0 home defeat by Manchester City last week.
Danilo Duvjak put Linz ahead following a corner in the 26th minute and Harun Sulimani doubled their lead on the stroke of halftime following a mistake by Uganda defender Ibrahim Sekagya.
Boris Arapovic put the team from the Regional Middle League - one of three leagues which comprise the third division - 3-0 ahead in the 65th minute before Austria striker Roman Wallner scored a stoppage time consolation for Salzburg.
Wallner also had a 94th-minute penalty saved by David Wimleitner.
Previously known as Austria Salzburg, the club was bought and rebranded by the Red Bull soft drinks company in 2005 amid protests by their fans but with ambitions of becoming a force in European football.
Salzburg have won three Austrian titles since but, despite spending around 200 million euros, have failed to qualify for the Champions League.
Salzburg have been knocked out in the Champions League qualifiers four times in the last five seasons and this year were eliminated by Hapoel Tel Aviv.
They have also made a poor start in the league, taking five points from their first five games.
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