The former WAFA midfielder was thrown into the game by manager Jesse Marsch in the 78th minute as he replaced Zlatko Januzovic in their 4-3 defeat to the European Champions.
Senegal forward Sadio Mane struck inside 10 minutes, sweeping home at the near post.
Andrew Robertson turned in a cross from Trent Alexander-Arnold before Salah poked a third under keeper Cican Stanokovic.
But Salzburg began their fightback when Hwang Hee-chan got the better of Virgil van Dijk before scoring with a powerful strike.
The visitors reduced the deficit further when Takumi Minamino volleyed in and the away fans erupted when substitute Erling Braut Haaland tapped in an equaliser - his 18th goal of the season.
Salah finally got Liverpool over the line when he latched on to Roberto Firmino's header and scored with a fierce strike. Read Full Story
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