Goals from Jon-Paul Pittman and John Mousinho either side of Murray's overhead kick had put Wanderers 2-1 up at the break. But Nicky Forster levelled soon after the break and Murray helped himself to a second-half treble to hand boss Gus Poyet his first win in four games.
Mousinho hit the foot of the post with a long-range shot before Pittman drilled Wycombe ahead from close range in the 27th minute following a goal-mouth scramble.
Murray equalised for Brighton in the 35th minute with a brilliant eight-yard overhead kick from Elliott Bennett's cross, but Mousinho tapped in from two yards to restore the Chairboys' lead four minutes later after goalkeeper Peter Brezovan inexplicably dropped Tommy Doherty's deflected free-kick.
But Forster volleyed in Gary Dicker's cross to equalise four minutes after the break before crossing for Murray to head the Seagulls 3-2 up in the 55th minute.
Murray turned Chris Westwood superbly in the box before firing in Brighton's fourth goal in the 70th minute and then took his season's tally to eight goals by heading in Dean Cox's cross 10 minutes from the end.