Former Hull and Reading predator Forster struck his third goal of the campaign from point-blank range after substitute Dean Cox set him up with a perfect cross.
It was hard work for the Seagulls to gain maximum points against a Wanderers side that defended stubbornly throughout.
Brighton should have doubled their lead at the death when substitute Gary Hart missed an open goal after being fed by Cox.
Liam Dickinson had earlier just failed to connect in front of goal following a fine run by winger Elliott Bennett.
Midfielder Arron Davies had Brighton's best chance when his goalbound shot was pushed around the post by goalkeeper Scott Shearer from Forster's pass.