The Blue and Gold delivered a tense first half against the reigning premiers, but were unable to contain their opponents in the face of a ten minute sin-binning and the experienced Melbourne attack.
From the first hit up by Club Captain Tim Mannah, the Eels had no trouble making ground down the middle of the field in the first half, and the Blue and Gold turned to the left wing to capitalise on their field position.
A sweeping play saw Semi Radradra open the scoring in the corner in the third minute of play, and the Fijian flyer almost made it a double more than once in the first half thanks to his burgeoning combination with Ryan Morgan and Jake Mullaney.
The Storm responded by peppering the Eels defensive line with charges from big second-rowers Kevin Proctor on the right and Ryan Hoffman on the left.
Persistence paid off on a third attempt, with Ryan Hoffman running over to put the Storm's first points on the board.
Just fifteen minutes in the Storm put up a bomb for winger Sisa Waqa to collect, running a fantastic line and handing off the ball for Billy Slater to bag a four-pointer.
The Melbourne forwards continued their onslaught, with the Eels line working overtime to contain Hinchcliffe, Ryles, Proctor and Hoffman.
And at both ends the referees kept their whistles out, with both teams conceding a brace of penalties, and neither clearing a 75% completion rate on their attacking sets. Even Melbourne dynamo Cooper Cronk was out of sorts at moments, sending a kick out on the full for a handover.
The Storm game plan paid off one last time before the halftime whistle, as Ryan Hoffman scored his second try for the evening, falling over the line in the 37th minute.
A fiery start to the second half saw Parramatta's Joseph Paulo sin-binned for ten minutes for a professional foul on Justin O'Neill, pulling the Storm winger down just short of the try line, and the Storm capitalised immediately through Will Chambers.
Down to a twelve-man defensive line the Eels held off line breaks from the Storm's Hoffman and Chambers, but fullback Billy Slater's momentum carried him over the tryline in the 59th minute to bring the home side's lead to 24 points.
Captain Cameron Smith extended the lead, sending Kenneath Bromwich over for his first NRL try, and Billy Slater followed suit with his third try for the evening.
As the clock wound down, Melbourne debutant Tim Glasby found space and was too big to stop, scoring a try in his first NRL game, and Jesse Bromwich joined his brother Kenneath on the try-scoring list with a late four-pointer.
Will Chambers bagged a double thanks to a late four-pointer, and Maurice Blair added a try of his own as the Storm recorded their biggest ever win over the Eels.