Brighton's top scorer came off the bench to score two goals and set two up as his side followed up their first home league win against another of the top sides, Leicester.
Murray, previously sidelined by a thigh problem, was only passed fit enough for the bench a few hours before kick-off.
Brighton were forced to bring him on less than half-an-hour into the contest when Adam Virgo suffered blurred vision from a bang in the eye.
Murray opened the scoring in atrocious conditions at the Withdean Stadium, a minute before the break, turning Matt Richards' pass to score with an angled left-footed drive.
Millwall began the second half brightly and were rewarded when Tresor Kandol combined with veteran marksman Neil Harris to score with a curling effort via a post.
The game turned on a penalty decision by Premier League referee Alan Wiley, who decided Brighton striker Joe Anyinsah had his shirt pulled inside the box by Tony Craig.
Murray's resulting penalty was saved with his legs by keeper David Forde as he dived to his right but the ball broke kindly for Murray to slot home the rebound.
The former Rochdale marksman set up on-loan Leeds midfielder Bradley Johnson for his third goal in two games, eight minutes later.
Murray made space for himself down the right before picking out Johnson's run through the middle and he fired a left-foot drive past the helpless Forde.
The best goal was reserved until last, Brighton finishing Millwall off with a superbly crafted goal nine minutes from time.
Richards started it with a raking diagonal ball to Murray. He took his time by the corner flag before delivering an inch-perfect cross for the diminutive Dean Cox to crash a volley into the roof of the net.