Backstrom, who had 24 saves, had been 14-9-5 with a 1.88 goals-against average and .933 save percentage against the Flames.
"This whole game we took the wrong approach into how we're going to score goals. We shouldn't play like that," Wild coach Mike Yeo said. "This was not the way we're supposed to play the game."
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.
"We need to win some games," Hartley said. "I told the players this morning, the win one, lose one is not going to work in an 82-game schedule and it certainly is not going to work in a condensed schedule."
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.