Adam El-Abd's first goal in two years gave the Seagulls an early lead before Adam Miller equalised in the 49th minute, but Josh Gowling's red card for a foul on Murray was not punished by the visitors.
Struggling Gillingham made the worst possible start when an unmarked El-Abd headed in Elliott Bennett's corner with five minutes gone.
The Gills did draw level early in the second half as Miller latched onto Rene Howe's flick on before slaloming his way through the Seagulls defence to fire home.
Murray missed two gilt-edged chances to restore the visitors' advantage and with nine minutes remaining home substitute Chris Dickson hit the post.
With time almost up Gowling was sent off for pulling back Murray in the area but the Brighton striker saw his spot-kick expertly saved by Julian.