Melbourne needed all their class to hold off a tremendous display by Leeds and become the first Australian team to claim a third victory in the annual Probiz World Club Challenge.
The Rhinos were never in front but staged two thrilling fightbacks to remain in contention throughout a compelling contest at Headingley before falling just short in their attempt to secure what would have been a record fourth victory.
Leeds' spirited efforts were typified by 35-year-old former England captain Jamie Peacock, who rolled back the years with a vintage performance on his record sixth appearance in the global challenge.
Second rower Tohu Harris, one of three Melbourne debutants, full-back Billy Slater and prop Jesse Bromwich scored the tries that enabled the Australian champions to complete their second win over the Rhinos in four years.
Despite the freezing temperature and an intimidating atmosphere created by a capacity 20,400 crowd, the Storm were the first to settle and dominated the opening quarter.
The Rhinos were continually pegged back deep inside their own half by the clever kicks of Kangaroos duo Cooper Cronk and Cameron Smith, who pulled all the strings for the visitors.
Kallum Watkins initially looked a secure full-back replacement for the injured Zak Hardaker, pulling off a tremendous tackle to bring down Slater and comfortably taking one high ball from Cronk but, when he fumbled another, it presented Smith with an easy kick to open the scoring on 12 minutes.
It was no real surprise when Melbourne extended their lead seven minutes later, former Wigan second rower Ryan Hoffman taking Cronk's short pass to go between Kevin Sinfield and Carl Ablett and sending the supporting Slater over for the first try.
Smith's second goal made it 8-0 but, even with scant possession, Leeds had begun to demonstrate their attacking prowess and they gradually clawed their way back into the game.
Centre Joel Moon had been bundled into touch early on by Slater and Danny McGuire, on his 300th appearance for his home-town club, cut through the first line of defence only to put out a forward pass while winger Ryan Hall was literally thrown back from the line.
Clearly up for the challenge, Leeds' passions were further aroused by a late tackle by Melbourne prop Jason Ryles on Sinfield and they eventually cracked the visitors defence on 28 minutes when Rob Burrow, Sinfield and McGuire all combined to give Hall a chance at the corner to which he produced a typical clinical finish.
Sinfield's touchline conversion made it 8-6 and he drew his side level on the stroke of half-time with a penalty but the Rhinos would have held a useful lead but for a couple of blunders.
Watkins sliced effortlessly through the heart of the Melbourne to create a clear-cut chance for Burrow but the hooker inexplicably dropped the ball while McGuire also failed to take Stevie Ward's offload with the line breached.
The misses began to look especially costly when the Storm exploded into life after the break, scoring two tries within seven minutes of the resumption.
Bromwich swatted aside the attempted tackles of Paul McShane and Watkins to charge over within four minutes of the re-start and Leeds had barely recovered from that shock when their visitors struck again.
After playing a direct game for the first 40 minutes Melbourne suddenly went wide with devastating effect as winger Sisi Waqa collected McGuire's kick 10 metres from his own line and Harris finished off the counter-attack moments later by crossing at the corner.
At 18-8, there looked to be no way back for the Super League champions but Hall had different ideas.
He collected Sinfield's pinpoint kick to the corner, found his partner Moon and took a return pass to get back rower Jamie Jones-Buchanan over for the Rhinos' second try.
Sinfield's third goal cut the deficit to just four points and, with Peacock once more leading the charge, Leeds pressed for the winning try.
However, Melbourne's superb defence stood firm and they even had late tries by winger Mahe Fonua and England stand-off Gareth Widdop disallowed as they clung on for a deserved victory.