Alex Oxlade-Chamberlain opened the scoring on the south coast before Naby Keita made it 2-0 shortly before the break.
Salah completed the scoring in the second half and the Reds went on to record their first clean sheet in 14 matches.
"The most used word in the dressing room at the moment is 'clean sheet'... finally!" Jürgen Klopp reacted post-match. "All round, nearly perfect day."
Watch the highlights of the win again in the latest instalment of our Replayed series on YouTube, which looks back on each 2019-20 league match every weekday.