Tranmere, under pressure early on, had a penalty appeal waved away midway through the first half when Charlie Barnett was brought down by Andrew Whing.
The struggling Seagulls were denied a spot-kick after 65 minutes when Whing's throw-in into the area appeared to strike the hand of defender Ian Goodison.
Rovers almost snatched victory late on when Ben Chorley's goal-bound shot produced an excellent save from recalled goalkeeper Michel Kuipers while Brighton striker Craig Davies was also denied by a terrific save from Danny Coyne as the match finished in stalemate.
Dean Cox should have hit the target in the first minute for Brighton when he fired a foot wide after Lloyd Owusu flicked on a long free-kick by Whing.
Brighton got on top early on and Rovers keeper Coyne came to his side's rescue by tipping over a fierce drive from Cox in the 17th minute. Striker Ian Moore had an opportunity to put Rovers ahead following good work by Steve Jennings and Bas Savage, but Kuipers saved his low goal-bound attempt.