Endeavour comfortably outweighed quality in a poor first half in which Vale held the upper hand.
Luke Rodgers failed to get hold of his shot after good work by Craig Rocastle and Paul Edwards created an early chance.
But the action didn't heat up until the closing stages of the first period when Vale twice went close to breaking the deadlock.
Brighton full-back Andy Whing cleared off the line after David McGoldrick met Shane Tudor's 42nd minute corner with a powerful header.
And in the same attack Michael Kuipers pulled off the first save of note when he flung himself to his left to beat out a Rocastle shot.
Brighton boss Dean Wilkins must have been disappointed with his side's lacklustre efforts in the first period and his harsh words during the interval did spark an improvement.
Revell squandered their first chance when he headed across goal rather than for the target from a Dean Cox free-kick.
But Revell made amends in the 64th minute when he gave the visitors the lead following a catalogue of errors in the Vale defence.
Vale skipper George Pilkington sliced his attempted clearance and Joe Anyon was beaten in the air by Albion substitute Nathan Elder.
Elder's header was virtually his first touch but it proved crucial as Revell was on hand to prod the loose ball into an empty net.
Vale's task was made much tougher when debutant Adam Eckersley, on loan from Manchester United, was sent off for a foul on Jake Robinson resulting in his second booking of the match.
And Brighton could have rubbed salt in Vale's wounds in the closing stages when Elder squandered two good chances.