The home side had the consolation of a first clean sheet in the League in front of their own fans since August.
And they would have been celebrating all three points if they had more fire power up front.
Brighton were grateful for a goal-line clearance early on from Kerry Mayo.
The experienced left-back, returning to the team after suspension and injury, dropped back onto the left hand post to clear a goal bound free kick from 20 yards by Vale midfielder Paul Harsley.
It was the closest either side came to scoring in a dull first half, although Brighton missed a good chance to go in front moments before the interval.
A right-wing cross from Jake Robinson picked out a run into the penalty area by captain Dean Hammond but the nine-goal midfielder headed straight at Vale's young keeper Joe Anyon when completely unmarked.
Brighton improved after the break once Manager Dean Wilkins moved Robinson out to the left-wing and Dean Cox into a free role in the middle.
A clever back heel by Cox released Robinson for an angled drive which beat Anyon but rolled inches wide of the far post.
Vale went close to breaking the deadlock when a glancing header by Luke Rodgers on his debut following a £30,000 move from Crewe, narrowly missed the target.
It was a rare opportunity for Vale as Brighton continued to carve out chances.
Another header by Hammond from a Cox corner was parried by youngster Anyon and eventually scrambled clear.
Brighton had two further opportunities to take all three points in the closing stages.
Former Billericay striker Nathan Elder, brought on in place of Joe Gatting, had a left-foot shot from eight yards blocked by Anyon.
Cox also drove just wide from the edge of the box as Vale held on for a hard earned stalemate.