The visitors had much of the early possession but failed to make it count and promotion-chasing Preston proved too clinical in the end.
Michael O’Connor came close twice for Vale, as did Mark Marshall who saw a shot brush a post after beating Scott Wiseman down the left-hand side.
But the hosts began to grow into the game as the first half progressed and Joe Garner saw his bicycle kick palmed away.
However, it was Gallagher who opened the scoring three minutes before half-time, pouncing on a loose ball after good work by Garner to smash home.
The game threatened to boil over after the break with Garner booked for an off the ball incident, and with just over 10 minutes to go Vale centre-back Stephane Zubar was shown red card for striking Garner in the face.
Preston doubled their lead almost instantly after the dismissal, Browne running through from midfield before seeing his deflected strike trickle past goalkeeper Chris Neal.
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