Albion went one up on 20 minutes after Simon Adingra dispossessed Alexis Mac Allister when keeper Alisson played a poor ball out to him.
Adingra played a quick shot to put the Seagulls in front.
But the Reds hit back with a Mo Salah double shortly before the break.
They equalised against the run of play after 39 minutes.
Lewis Dunk gave the ball away to Dominik Szoboszlai and the Hungarian fed it forward to Darwin Nunez.
Nunez moved it on to Luis Diaz whose ball in to Harvey Elliott was perfectly weighted for him to set up Salah to slot home.
The visitors took the lead from the penalty spot in the 44th minute when Bart Verbruggen played an awkward pass to Pascal Gross.
Szoboszlai tackled Gross who, in a desperate attempt to recover the ball, yanked down the Liverpool midfielder, allowing Salah to score from the spot.
