Tied 1-1 in the third period and with Jarome Iginla screening Niklas Backstrom, Chris Butler's slapshot from the blue-line was deflected on net by Iginla. Backstrom stopped that one, then sprawled to get his pad on Stajan's rebound.
But Stajan kept after the puck and jammed it over the line just inside the post at 7:19.
Stajan entered the night the Flames' leader in plus-minus at plus-5 and having been one of Calgary's most consistent players all year. Looking to find a spark, coach Bob Hartley moved him onto the top line where he centred Iginla and Alex Tanguay, who also scored.
Calgary (6-7-3) began the night in 14th place in the Western Conference, five points back of the Wild and Phoenix, who held down the final two playoff spots. The Flames get a chance to move two points closer to the Coyotes on Sunday night when they wrap up their three-game homestand.
Charlie Coyle, with his first NHL goal, scored the lone goal for Minnesota (8-7-2). The Wild split of its two-game trip through Alberta.
With Miikka Kiprusoff (knee) on injured reserve and missing his ninth game, Joey Macdonald made his third start and fourth appearance in the last five games. The 33-year-old, claimed on waivers from Detroit two weeks ago, made 30 saves to even his record at 2-2.
Backstrom had 24 saves. It was no surprise that he got the start considering his career 14-9-5 record against them along with 1.88 goals-against average and .933 save percentage.
Attempting to add more grit to his lineup, Flames coach Bob Hartley inserted hulking six-foot-four, 225-pound Akim Aliu.
His addition didn't have much impact early in the game, getting just three shifts in the first period. However, during a mostly uneventful second period, he did stir some noise from the sellout crowd of 19,289 when he stormed his way into the offensive zone and crushed Wild defenceman Clayton Stoner. No penalty was assessed on the play.
The other new body 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 re-direction.
Shortly after, Minnesota tied the game 1-1 when Coyle darted for the net and got his stick on a perfect feed from Pierre-Marc Bouchard.
Calgary took the lead 1:40 into the game on a sequence that began with a dangerous 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 defenceman Jay Bouwmeester, who had been caught up ice, retrieved the loose puck, turned, and sent a breakaway pass to Tanguay who made no mistake making 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) did not play. Clutterbuck was hurt Friday night 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 on goal but remains stuck at one goal. Dating back to last season, Iginla has two goals in his last 27 games.