Jurgen Klopp again named a strong line-up and granted Sadio Mane, Mohamed Salah, Andy Robertson, Georginio Wijnaldum, Joe Gomez, Neco Williams and Alisson an hour of game time.
The Premier League champion fell behind inside three minutes when Patson Daka caught Fabinho in possession and raced through to slot a cool finish past Alisson.
TRIAL FORM: Liverpool topples Stuttgart
Daka doubled his and Salzburg's tally 10 minutes later when he darted away from Virgil van Dijk and steered Mergim Berisha's square pass home.
A goal-line block from Albert Vallci kept Mane at bay before half-time, while Van Dijk was forced off after suffering a cut to his head following the restart.
Brewster scored in the 3-0 win over Stuttgart on Saturday and went on as one of seven changes after the hour mark. He fired into the roof of the net at the end of an intricate move to halve the deficit in the 72nd minute.
The 20 year-old striker, who spent the second half of last season on loan at Championship side Swansea City, looped an equaliser into an empty net from 20 yards after Alexander Walke raced off his line to deal with Oumar Solet's poor header and kicked a clearance straight at Curtis Jones.
Klopp's team will now return to England ahead of its Community Shield meeting with Arsenal on Sunday (AEST).