Home skipper Antony Kay was credited with the winner with a close-range effort after Chris Shuker saw a shot blocked after an Ian Moore shot rebounded off a post.
The visitors nearly had the boost of a second minute goal. Nicky Forster found the side-netting after getting the better of Ian Goodison following a long clearance.
At the other end, Chris Shuker was just over with a 20-yard free-kick and then flicked an effort wide from the edge of the box.
Tranmere made much of the first-half running but Chris Greenacre and Shuker had shots blocked as Albion defended doggedly.
The home side almost made the breakthrough five minutes before the break.
Visiting keeper John Sullivan did well to beat out a powerful strike by Kay before Greenacre headed just off target.
Forster with an angled effort went close soon after the re-start for Brighton, while at the other end Bas Savage headed well off target from a Shuker cross.
Home keeper Danny Coyne made a good save from Forster, who struck the outside of a post in the 61st minute.
Tommy Elphick and Andy Whing were excellent in the Brighton back four. Dean Cox was often in the thick of the midfield action and Forster worked tirelessly up front.
Shuker was always lively for Rovers and there were solid contributions from Kay and Ben Chorley.