With other team around them, such as Nottingham Forest, Southend, Leyton Orient, Walsall and Leeds all dropping points, this will certainly be seen as one point gained in what was always going to be a tricky test for the Wirral side.
Ronnie Moore again picked the same team that played in the last match, a 1-1 draw with Leyton Orient, as Chris Greenacre was once again kept on the substitutes bench.
From the start, chances were limited with sloppy passes and a lack of urgency combined with some decent defending meant each set of strikers failed to get a good chance.
Rovers had the first shot as Myrie-Williams cut in from the right but he put his weak effort well wide of the goal before Brighton started to take the upper hand.
For the next 20 minutes, if any team was going to score, it looked like it would be Brighton, although still there were no clear cut chances.
The Seagulls pushed forward and on numerous occasions, the wingers were given far too much space on the left as Sherriff drifted out of position whilst Andy Taylor failed to clear his lines a number of times as he had a shakey start to the game, invariably putting the visiting defence under more pressure with his poor clearances.
Brighton's first real chance came on five minutes but Forster's heavy touch took the ball too far as he tried to take the ball around the advancing Coyne whilst the home side had a number of other moves ended by either the offside flag or crosses hit straight at Danny Coyne.
Moore sent a flick header straight at Kuipers from near the penalty spot as he connected with Myrie-Williams' cross on the half hour mark before Brighton had a goal dissallowed on 33 minutes.
The home side won a corner on their right after Ian Goodison had blocked a cross out of play. The set-piece was put into the six-yard box from where former Rochdale striker Glen Murray bundled it home. However, with the home fans cheering, the referee ruled out the goal for a push by the Brighton number 17.
In the final ten minutes or so of the half, Tranmere began to get back in the game. Instead of playing the long ball, they passed the ball around on the surface and began to find openings in the Brighton defence.
Rovers won a string of corners, whilst Andy Taylor's low drive from the edge of the area forced Kuipers into a good save before Moore was flagged offside on the follow up, whilst Myrie-Williams had a shot deflected wide after he had once again cut in on to his left foot.
The second half started with Brighton applying the pressure, as they came close to getting the ball into the back of the net for a second time on 53-minutes.
Bowditch shot at Coyne but the Welsh international could only push the ball out as far as Forster who saw his rebound deflected over the bar.
From the resulting corner, Brighton came close yet again as former Coventry player Whing rose highest to met Cox's set-piece, sending a flick header just wide of the far post when only a touch was required to put it in the back of the net as the ball went right across the face of the goal.
Rovers though were beginning to look more and more in the game, with Myrie-Williams sending one shot wide from the left just before the hour mark after he had recieved Shane Sherriff's knock down.
Cox curled a free-kick narrowly round the post for Brighton and then Zola shot wide from inside the area on 70-minutes before Rovers should have had a penalty on the 75-minute mark.
Calvin Zola turned his man and managed to get into the area before being bundled down, but the inconsistent referee waved away the tackle, despite the defender clearly not winning the ball.
With six minutes left, Chris Greenacre finally replaced Calvin Zola upfront as Ronnie Moore looked to freshen things up in the last few minutes, but all the pressure in the closing stages was down the other end.
However, for all their pressure and the corners they won, the home side couldn't test Danny Coyne bar a header in the final minute from Forster which went straight at the Welsh international from 8-yards out.
The game therefore ended as a 0-0 stalemate, a result that keeps Tranmere sixth in the table and now two points ahead of seventh placed Leeds.
Jones' Man of the Match: For periods Rovers were sloppy, but the likes of Jennings, Goodison and Zola all had decent games for the away side. However, for me the most impressive player out there was Antony Kay, who commanded in the air at the back and didn't let a single thing past him all game.