Murray put the Seagulls ahead with a well-taken shot a minute before the break after an intelligent ball from defender Matt Richards.
Striker Tresor Kandol levelled with his fifth goal in nine league starts, but Murray struck again from the penalty spot when Tony Craig was adjudged to have tugged the shirt of right-winger Joe Anyinsah.
Goalkeeper David Forde dived to his left to block Murray's spot-kick but the former Rochdale forward followed up to tuck in the rebound.
Bradley Johnson made the game safe with his third goal in two games by impressively converting a Murray pass midway through the second half.
Dean Cox sealed Brighton's biggest league win of the season by thumping in another Murray cross nine minutes from time.