The Seagulls have now won only once in their last eight matches as Rovers came away with a hard-earned point to remain in sixth place.
The return of Dean Bowditch on loan from Ipswich could not inspire Brighton to victory but he was sharp and lively in the early part of the match.
Bowditch, whose loan stint on the south coast last season was interrupted by injury, linked up well with former Ipswich team-mate Nicky Forster.
Chances were few and far between for both teams, but Brighton nearly took a 20th minute lead in freak manner.
Full-back Andrew Whing blocked an attempted clearance by Tranmere centre-half Antony Kay just outside his own penalty area.
The ball ricocheted goalwards and keeper Danny Coyne had to change direction smartly to smother.
Brighton had the ball in the net in the 33rd minute when Glenn Murray headed in a Dean Cox free-kick but it was disallowed for a foul by the £300,000 purchase from Rochdale.
Rovers were not much of a threat in the opening 45 minutes but they almost went ahead against the run of play just before the interval.
A low drive through a crowded penalty area by Andy Taylor forced Brighton goalkeeper Michels Kuipers to save at full-stretch.
It was a similar story in the second half,with defences in charge.
Cox curled a free-kick inches wide of the far post.
Calvin Zola had Tranmere's best chance when Kuipers made a mess of punching clear a corner but the Congolese striker drove wide on the turn.
Brighton's long-serving defender Kerry Mayo almost snatched the points after coming on for Guy Butters in the closing stages.
Mayo met a free-kick from Matt Richards with a downward header which Coyne grabbed to maintain Tranmere's nine-point cushion over their hosts.