The Storm ran in three unanswered tries in the first half to set up the victory, with star fullback Billy Slater first on the scoreboard.
Dashing centre Justin O'Neill finished with two tries, scoring one in each half.
With the temperature 30 degrees-plus the Storm further turned up the heat on the Dragons, who haven't won in Melbourne since 1999.
Their losing streak there now stands at 12.
Slater and fellow big guns Cooper Cronk and skipper Cameron Smith played their usual leading hands, while young forwards such as prop Jesse Bromwich and debutant Tohu Harris impressed.
Melbourne took an 18-0 lead to the sheds at halftime, with O'Neill, Slater and five-eighth Gareth Widdop all touching down.
The margin could have been even greater but for a number of passes that failed to find their mark to the chagrin of coach Craig Bellamy.
Widdop's try came in the 28th minute after Dragons halfback Nathan Fien tried to put a kick through into the in-goal only for it to bounce up off the Storm player's foot - he scooped it up and charged 80m down-field.
The visitors opened the scoring two minutes into the second half when Cronk tried to throw a no-look pass that landed in the arms of Jamie Soward for another 75m run.
It was the only blemish in an otherwise stand-out game for Cronk.
Whether the heat was taking its toll or the cobwebs of a new season, O'Neill's second try was also scored from an intercept pass, with Dragons reserve hooker Cameron King the guilty party.
The Dragons did well to close the gap to 24-10 as winger Jason Nightingale caught the defence short out wide.
But the Storm delivered a knock-out punch with six minutes remaining when the ball went through nine sets of hands.
O'Neill could have dived across for a hat-trick but he sent the ball on to rising star Mahe Fonua.
Compounding the disappointment for the visitors, centre Chase Stanley was assisted from the field with what appeared to be a knee injury in the final few minutes.