The Pilgrims' defeat was their seventh on the trot and leaves them rooted to the bottom of the League One table following their 10-point deduction for calling in the administrators.
Murray put the Seagulls ahead with a simple finish in the 28th minute at the Withdean Stadium as Argyle were caught deep in their own box and the striker slipped the ball under goalkeeper David Button after Chris Wood's pass took a ricochet.
Murray set up Ashley Barnes just before the break with a hanging cross to the far post, but the former Argyle striker headed inches wide.
Wood doubled Brighton's lead four minutes before the interval with goalkeeper Button getting a hand to his shot from 25 yards, but being unable to keep it out and Murray rifled his second three minutes after the interval with a smart swivel-and-shot into the roof of the net.
Button thwarted a goalbound effort from Wood and Murray also had a shot blocked as Brighton dominated.
Substitute Francisco Sandaza sealed Brighton's comfortable victory in the third minute of stoppage time with a cool finish after a throughball from Gary Dicker.