They packed men behind the ball and soaked up everything that Blackpool could throw at them.
Home keeper Paul Rachubka only had one save to make throughout the match but it was a vital one.
He flung himself to his right to push away a goalbound screamer from Jake Robinson in the 70th minute.
The first half was best forgotten with the quality of football often dire and both sides giving away far too much possession.
Blackpool had the better of the chances with Adrian Forbes and Claus Jorgensen both getting in chances.
Jorgensen's effort was bravely blocked on the line with his body by Brighton skipper Guy Butters in the 35th minute.
Blackpool improved in the second period, although they tended to over elaborate in midfield and waste opportunities at set pieces far too often.
Seasiders manager Simon Grayson used three attackers as substitutes in a bid to break the deadlock, but Brighton were quite content to start running the clock down in their bid to take away a point.
Late pressure from Blackpool saw chances fall to Jorgensen once again.
In the 65th minute his free-kick was collected at full stretch by Scott Flinders and then the keeper did well to make a reaction save from Keigan Parker before denying Jorgensen with four minutes to go with a low save to his left.