The Storm navigated periods of torrential rain to down the Warriors 26-10 on Friday night in Auckland.
Despite the testing conditions, Melbourne played high percentage football through the 80 minutes, making only seven handling errors and missing 17 tackles, to record their third-straight win at Mount Smart Stadium.
The Warriors' cause wasn't helped by losing captain Roger Tuivasa-Sheck to concussion in the 28th minute, but an ability to defuse kicks and win the physical battle in the middle of the park were the home side's major downfalls.
With the game only seven minutes old, Kenny Bromwich latched on to a pinpoint Cooper Cronk chip to open the scoring and pick up his try in four games against the Warriors, with Cameron Smith converting from in front.
After Melbourne were denied a second by the NRL Bunker a short time later, the Warriors scored twice in three minutes to take the lead.
The first was a stunning team effort, with Ata Hingano's initial kick deflecting back to the Warriors before a series of offloads led to another Hingano kick, which was claimed by Shaun Johnson and offloaded to a waiting Tuimoala Lolohea who slid over.
Johnson converted from the sideline, then scored one himself following a Storm error to overtake club legend Stacey Jones (674 points) as the Warriors' all-time leading scorer.
With 15 minutes to go in the half an untimely slip from Lolohea saw him fail to defuse a short kick, gifting Cheyse Blair with the easiest of four-pointers.
Cameron Smith converted to achieve a unique record of his own; the first Queenslander and forward to reach 2000 NRL Telstra Premiership career points.
The Storm led 12-10 at the break.
A strong carry from Nelson Asofa-Solomona set the tone for Suliasi Vunivalu's try three minutes into the second period, with classy touches from both Cronk and Cameron Munster in the lead-up.
The Warriors should have reduced the deficit on 55 minutes when Solomone Kata fumbled the ball over the line, but instead the Storm maintained momentum and kicked a penalty through Smith to extend the gap out to 20-10.
The visitors soaked up a series of late attacking raids from the Warriors, before icing the result with a Cronk try under the posts, which Smith converted for a final score of 26-10.
Melbourne Storm 26 (Kenny Bromwich, Cheyse Blair, Suliasi Vunivalu, Cooper Cronk tries; Cameron Smith 5 goals) defeated New Zealand Warriors 10 (Tuimoala Lolohea, Shaun Johnson tries; Johnson 1 goal) at Mt Smart Stadium. Half-time: 12-10. Crowd: 9,811.