While they were slick with ball in hand, the Raiders' biggest improvement came without the ball. They looked much more solid defensively.
Melbourne opted to rest Queensland State of Origin skipper Cameron Smith after a hectic couple of months during the representative season and his heroic performance for the Maroons on Wednesday night.
The visitors struck first when centre Blake Ferguson outjumped Anthony Quinn from a crossfield kick. From their next set, the Raiders went wide early and Reece Robinson created and then finished a nice backline move.
The Raiders continued to play an expansive brand of football, offloading almost at will and it led to more points.
Both wingers - Edrick Lee and Sandor Earl - finished sweeping backline moves that any side would have been proud of.
Storm centre Justin O'Neill collected his second try of the night just before the halftime siren to keep the home side in touch at the break.
Lee, who finished with three tries on the night, scored his second straight after halftime and the Raiders sealed the match when Jarrod Croker scored from a nice offload midway through the second spell.
The result meant the Storm lost back-to-back games at home for the first time since 2005.
They remain atop the standings despite the loss and will welcome back Smith and brilliant fullback Billy Slater from injury for next weekend's match against the Cowboys.
If the Raiders are to take advantage of this little bit of momentum and qualify for the playoffs, they need to win their next three matches against sides in or around the top eight.
They face the Titans, Sharks and Knights over the next three weeks.
Storm 12 (J. O'Neill 2 tries; G. Widdop 2 goals), Raiders 40 (E. Lee 3, S. Earl 2, B. Ferguson, R. Robinson, J. Croker tries; J Croker 4 goals). Halftime: Raiders 20-12