The Seagulls went into the match knowing victory would guarantee safety and substitute Forster settled the issue 17 minutes from time.
Stockport, with nothing to play for, made things difficult for Brighton throughout and, before Forster's strike, the Seagulls rarely threatened to find a way through the visitors' defence.
Goalkeeper Michel Kuipers came to Brighton's rescue after 29 minutes by parrying a goal-bound shot from Oli Johnson after good work from Michael Rose.
On-loan midfielder Dicker, facing his parent club, headed a Dean Cox corner wide for Brighton shortly before the break.
Albion almost broke the deadlock a minute before the interval when substitute Calvin Andrew's header bounced onto the top of the bar after keeper Logan blocked a shot from Cox, but Forster's strike secured their safety.