The Egyptian set a record for most goals scored in a 38-match season as Liverpool ended 2017/18 unbeaten at Anfield.
The EA SPORTS Player of the season broke the deadlock on 26 minutes with his 32nd goal of a superb campaign.
Dejan Lovren doubled Liverpool's lead when he headed in Andrew Robertson's cross just before half-time.
Salah then turned provider by passing for Dominic Solanke to net for the first time in the competition, before Robertson made it 4-0 late on.
In finishing fourth Liverpool qualify for next season's UEFA Champions League ahead of their final in that competition in two weeks.
Brighton finish 15th in their debut PL campaign.