Winger Jason Nightingale got outside of Will Chambers to cross in the sixth minute before Benji Marshall and Gareth Widdop engaged in some clever to and fro that ended with Marshall diving across for their second.
That try seemed to shock the Storm and they sent the ball wide two minutes later with Slater finding Koroibete for a try.
The Fijian flyer was in again seven minutes later when he again burnt Dugan thanks to a long ball from Slater.
Two penalty goals from skipper Cameron Smith put the home side ahead with two minutes left in the half.
Melbourne looked like they would run away with the match when prop Kenny Bromwich crossed early in the second stanza after his brother Jesse magically managed to pop a pass.
That try had some extra sting because it came off the back of a penalty that should have gone the other way with Chambers pushing Jack de Belin in the play the ball.
The Dragons refused to go away and threatened the tryline as the clock wound down and Dugan tried to claim a try but the ball was already dead.
-AAP