Adam Boyd gave Pools an early lead in the sixth minute with a shot on the turn but Liam Dickinson levelled with a fine strike from the edge of the penalty area after 27 minutes.
Veteran frontman Forster put Brighton ahead from close range six minutes before the break but poor defending allowed Andy Monkhouse to make it 2-2 after 44 minutes.
It got worse for the Seagulls in first half stoppage time when Richie Jones struck after being set up by substitute Colin Larkin.
Forster took his seasons tally to nine two minutes into the second half when he converted Elliott Bennett's cross.
Both sides had chances to take maximum points, and Brighton keeper Graeme Smith saved from Denis Behan before Brighton winger Bennett hit a left foot drive inches wide.
Boyd found himself in a good position late on but mis-hit his shot with only Smith to beat.