Slater was less impressive, throwing an intercept that resulted in a 95-metre run for Morris's first try, which opened the scoring in the seventh minute.
His second was a similar effort, a 90-metre intercept in which he benefited from a mistake from one of Melbourne's other superstars - this time halfback Cooper Cronk.
The Dragons led 18-0, following tries to Morris, Beau Scott and Trent Merrin, with five minutes left before halftime when the Storm hit back in emphatic fashion.
Back-rower Kevin Proctor and centre Will Chambers punched holes in the Dragons left-handside defence to reduce the halftime lead to just six.
But Morris erupted to start the second half, scoring the second and third of his tries for the night to take his tally to 26 in 23 games at the Wollongong venue.
It was the end of their point-scoring for the night, but was still their biggest offensive output since their Anzac Day victory over the Sydney Roosters in round eight.
The Dragons managed to cling on for the final half an hour, producing some solid defensive displays the Storm were only able to breach their tryline through a scrappy try to lock Ryan Hinchcliffe.
Further souring the night for the Storm, Proctor was placed on report for a lifting tackle while Cronk could come under the microscope for a chicken wing tackle on Ben Creagh in the 47th minute.
- AAP