Brian Rolston and Mikko Koivu scored shootout goals after contributing power-play goals in regulation for Minnesota, and Fernandez - who made a season-high 38 saves - denied Kristian Huselius on the final attempt to earn his second straight win after a miserable stretch.
The Wild have played a league-high nine shootouts, winning seven.
Rhett Warrener and Jarome Iginla scored second-period goals for the Flames, who got 25 saves from Miikka Kiprusoff but were done in by a shaky first period.
Fernandez's last save before the shootout might have been the best, when he alertly pounced on Chuck Kobasew's wraparound shot with 39 seconds left in overtime.
This was the first of eight matchups between these Northwest Division foes, a so far mediocre but tight bunch in which six points separate first-place Edmonton and last-place Colorado. Calgary and Minnesota have been heading in opposite directions since early November, with the Wild going just 5-9-2 in their last 16 games.
Among all NHL teams with winning records, the Flames have the worst record away from home at 3-7-3. Despite 10 wins in their last 13 games, they reverted to their recently shoddy road ways in the first.
The biggest problem was taking penalties, six of them in the first 16 1/2 minutes, that helped the Wild snap out of their power-play slump.
Rolston sent a perfect cross-ice pass to Koivu, who slapped the puck in from the right circle to give Minnesota an early lead - and its first man-advantage goal in the last five games.
Less than two minutes after that, Rolston showed off his hard slapshot - putting enough strength on the puck so that it trickled through Kiprusoff's legs and gave the Wild a 2-0 edge. They nearly got another one seconds later, during a 5-on-3, when a shot by Pascal Dupuis popped off the right post.
Warrener scored short-handed barely four minutes in, and then Iginla scored his 300th career goal about two minutes later by muscling past Martin Skoula on a power play and sneaking the puck through Fernandez's legs. Iginla's display was made more impressive by the holding penalty that was simultaneously called on Skoula.
The Flames kept up the pressure in the third period, peppering Fernandez with 14 shots. But the Wild got their defence back on track - highlighted by the killing of a 5-on-3.
Notes: Fernandez had two second-period penalties, for delay of game and high-sticking. The last time he had two penalties in a game was nearly four years ago. ... Iginla has scored in four straight games. ... The Wild got enforcer Derek Boogaard (ankle) back from an eight-game absence, but their lines are still banged up. Center Pavol Demitra missed his eighth straight game with a concussion, and star right wing Marian Gaborik has been out since Oct. 20 because of a strained groin. Centre Wes Walz (hip) also sat out for the eighth consecutive game.