Carlisle who crashed to their third home defeat of the season, had most of the game but were ineffective in the final third of the pitch and 36-year-old Forster's quicksilver skills gave them a lesson in finishing.
The home side began promisingly enough but it was Albion who struck first in the fourth minute.
Carlisle twice failed to get the ball clear with headers and when it dropped to Forster in the box the Brighton forward took advantage of the space he was allowed to coolly lob past keeper Lenny Pidgeley in to the corner of the net.
Forster's pace continued to trouble the Carlisle defence although visiting keeper Michel Kuipers had to be alert to tip a wayward header from his own central defender Tommy Elphick over the bar.
It was all Carlisle after the break but the Cumbrians were stunned by a second Brighton goal in the 66th minute when Liam Dickinson found room to cross from the left and Forster nipped in ahead of Pidgeley to prod home from a couple of yards out.