Iginla scored the go-ahead goal with 2:27 remaining to lift the Flames to a 3-2 victory over the Stars on Wednesday night.
With the game tied at 2, Daymond Langkow backhanded a pass in front of the net to an unchecked Iginla, the former Dallas first-round draft pick who fired his 38th goal of the season past Stars goaltender Marty Turco.
"It's big win against a team that plays well at home," Iginla said. "It's something to build on."
Stars defenseman Stephane Robidas left his assignment on Iginla and tried to check Langkow, who was set up behind the net. That made it easy for Iginla to notch his eighth winner of the season.
"I don't know how you can leave Iginla alone in front of the net, but we did," Stars coach Dave Tippett said.
Said Robidas: "The puck went behind the net and we lost a little bit of composure there. I should have stayed in front and tried to block that pass. It's my bad there. I should have made sure that pass doesn't come back in front, and I was a little bit too aggressive there."
Alex Tanguay scored twice for the Flames, including a short-handed goal early in the third period, breaking a 16-game drought.
Curtis Joseph stopped 29 shots in his third game for the Flames, who have won four of their last six.
Joseph registered his 447th career victory, moving into a fourth-place tie with Terry Sawchuk on the career list.
"This feels good," Joseph said. "To be next to someone like Terry Sawchuk is a great honor."
Calgary lost at Los Angeles and Anaheim in the middle of the road trip by a combined score of 10-5 before taking the final two against Phoenix and Dallas on consecutive nights.
"We had two bad games there, but this makes it a positive finish against two teams that play well at home," Iginla said.
The Flames didn't get to their hotel in Dallas until 3:30 on Wednesday morning, but they responded with a performance that pleased coach Mike Keenan.
"It was just on pure effort," Keenan said. "That's a real good sign. To see an effort like that .... I'm really proud of the guys."
"We just made some crucial errors at bad times and didn't create enough chances," Tippett said.
With the game tied at 1 and Dallas on a power play that began when Craig Conroy was penalized for hooking 3 seconds into the third period, Calgary defenseman Cory Sarich cleared the puck when it was inches from going over his team's goal line and passed to Tanguay.
Tanguay skated up the middle and beat Turco from the high slot 30 seconds into the period for his 13th goal to give the Flames a 2-1 lead.
But the Stars came back to tie it at 2 on Norstrom's power-play goal from beyond the left circle at 1:57, his first of the season and first since Jan. 13, 2007 for the Los Angeles Kings.
Calgary took a 1-0 lead at 13:29 of the opening period when Tanguay backhanded a loose puck past Turco from the right circle with Robidas serving a tripping penalty.
Hagman needed only 16 seconds of the second period to score his 22nd of the season and tie it at 1 on a shot from the left circle that got through Joseph's pads.
D Sergei Zubov (groin, foot) and D Philippe Boucher (shoulder) are still out for Dallas. There is no timetable for them to get back in the lineup, although both are expected to return to the ice before the end of the regular season. Zubov missed his 15th straight game and Boucher has been out since Dec. 5. ... C Stu Barnes also was out for Dallas with a partially torn retina. Barnes will miss between a week and 10 days. ... RW David Moss (ankle) is out for Calgary. ... Flames D Adrian Aucoin assisted on Tanguay's first goal, the 200th assist of Aucoin's career. ... Hagman has four goals in four games against Calgary this season.