Fernandez stopped two of the four shots he faced in the shootout, and the Wild made Luongo look silly after he was stellar in regulation. Luongo made 34 saves before the tiebreaker, including a brilliant game-saving stop on a breakaway by Todd White in overtime.
But Mikko Koivu beat him in the second round of the shootout, and after Jan Bulis fired a shot into Fernandez's pads, Nummelin came in slowly, hesitated and lifted a backhander over Luongo's glove to win it.
Luongo saved just one of four shots in the shootout, while Markus Naslund and Brendan Morrison scored for the Canucks. Vancouver's Taylor Pyatt had a goal in regulation.
Brian Rolston scored for the Wild.
These teams have forged quite a rivalry the past few years, especially after the upstart Wild beat the heavily favoured Canucks in the second round of the 2003 playoffs en route to a stunning run to the Western Conference finals.
But the Canucks and Wild made wholesale changes in the offseason and brought entirely new looks into the Xcel Energy Center on Tuesday night.
Vancouver got rid of agitators Todd Bertuzzi and Jarkko Ruutu, two of the biggest targets for Xcel angst, let Ed Jovanovski leave in free agency and replaced hard-nosed coach Marc Crawford with Alain Vigneault.
They also added Luongo, one of the NHL's top netminders, shoring up the team's biggest weakness in a trade with Florida for Bertuzzi and defenceman Willie Mitchell.
The Wild went on a surprising spending spree, forking out millions for Mark Parrish, Keith Carney and Kim Johnsson, trading for Pavol Demitra and signing star Marian Gaborik to a contract extension.
Despite all the changes, the game had a familiar feel. Up and down the ice. Few solid scoring chances. Aggressive checking. Close game.
The Canucks finally got on the board midway through the second period, when Daniel Sedin set up behind Minnesota's net, slipped a pass underneath Wes Walz's stick to feed Pyatt, who sneaked in unchecked near the right circle.
Fernandez didn't stand a chance, and watched the puck get past him high on the glove side to make it 1-0.
But Fernandez rebounded from an unusually poor showing on Saturday against Nashville. The Predators scored three goals on their first six shots, and coach Jacques Lemaire yanked Fernandez after the first period of a game the Wild eventually won 6-5.
This time, it was the Wild offense that struggled for most of the game.
After not getting many chances in the first two periods, they put the pressure on with two power plays in the third, finally breaking through with a fluke goal on their second chance.
Rolston caught the Canucks on a change and crept in on Luongo's left side just under 12 minutes into the period. He shoveled the puck toward the slot, and it hit off Vancouver defenceman Lukas Krajicek's skate and ricocheted through Luongo's legs to tie the game.
Notes: The game started at 8 p.m. Central time, an hour later than normal for Wild home games, to accommodate Canadian television. ... Vancouver C Ryan Kesler left the game late in the second period after getting walloped by D Kurtis Foster. Kesler wobbled off the ice and didn't return.