Jürgen Klopp's side trailed to a Luka Milivojevic penalty at the interval, but Sadio Mane levelled the score early in the second half.
And Salah struck for the 37th time this season six minutes from the end to complete an important comeback for the visitors in the Premier League clash at Selhurst Park.
See the story of the game in photographs below...
Images brought to you by Western Union, official principal partner of Liverpool FC