With the game tied in the third period, Jarome Iginla screened Wild goalie Niklas Backstrom as Chris Butler's slap shot from the blue line was deflected on net by Iginla.
Backstrom stopped the initial drive and sprawled to get his pad on Stajan's rebound, but Stajan jammed the puck over the line just inside the post at 7:19.
Stajan entered as the Flames' leader at plus-5, and he has been one of Calgary's most consistent players this season.
Looking for a spark, Calgary coach Bob Hartley moved him to the top line where he centered Iginla and Alex Tanguay, who also scored.
Charlie Coyle, with his first NHL goal, scored for the Wild, who split their two-game trip through Alberta.
Calgary began the night in 14th place in the Western Conference, five points back of the Wild and Phoenix, who are currently in the last two playoff positions.
The Flames will have a chance to move two points closer to Phoenix on Sunday night when they host the Coyotes and wrap up a three-game homestand.
With Miikka Kiprusoff (knee) out for a ninth game, Joey MacDonald made his third start and fourth appearance in five games for Calgary. The 33-year-old MacDonald, claimed on waivers from Detroit two weeks ago, made 30 saves to even his record at 2-2.
Backstrom, who had 24 saves, had been 14-9-5 with a 1.
Attempting to add more grit to his lineup, Hartley inserted hulking 6-foot-4, 225-pound Akim Aliu.
His addition didn't have much impact early as Aliu had just three shifts in the first period. However, during a mostly uneventful second period, he fired up the sellout crowd when he stormed his way into the offensive zone and crushed Wild defenseman Clayton Stoner.
The other new player in the lineup was Sven Baertschi (hip flexor), who returned after missing 11 games.
Baertschi showed glimpses of his speed early and nearly gave the Flames a 2-0 lead in the first period when he was set up at the far post on a perfect feed from Jiri Hudler. However, Backstrom stretched across and got the tip of his pad on the redirection.
Minnesota tied it 1-1 when Coyle darted for the net and got his stick on a feed from Pierre-Marc Bouchard.
Calgary took the lead 1:40 in off a sequence that began with a 2-on-1 rush by Minnesota.
Dany Heatley flipped a pass across the slot to Miikko Koivu, whose attempt at a one-timer came up empty with the puck bouncing over his stick.
Flames defenseman Jay Bouwmeester, who had been caught up ice, retrieved the loose puck, turned, and sent a breakaway pass to Tanguay, who made a slick move to his forehand to fool Backstrom for a shot under the crossbar.
Stajan capped the scoring with a shot into an empty net.
Notes: Roman Cervenka was a healthy scratch for the Flames. ... It was the first time in nine games Minnesota has scored a first-period goal. ... Minnesota RW Cal Clutterbuck (thigh) didn't play. Clutterbuck was hurt Friday in Edmonton when Taylor Hall caught him with a knee, a play in which the Oilers forward received a two-game suspension. ... Iginla leads Calgary with 59 shots, but has only one goal. Dating to last season, Iginla has scored only two goals in 27 games.