"It feels good, but the most important thing is we came out with two points," said Begin, who sat out all of last season with a hip injury and hadn't scored since the 2010 playoffs. "We needed those points and that's a huge win. We've got to be proud of ourselves but we've got to bring the same intensity for the next few games."
Begin snapped a 3-3 tie with 9:30 remaining. After Chris Butler's slap shot from the left point was blocked in front, Begin outbattled two Stars defenders to get to the loose puck and fire a wrister that beat goaltender Richard Bachman.
"I didn't see the initial shot," Bachman said. "There were a lot of bodies in front, it kind of bounced around and kicked out to my right, and as soon as I saw that, the first instinct's to get the pad down, try and seal the ice. He kind of spun around and he got a little elevation on it."
It was the Flames' second victory over the Stars in five days, having won 7-4 in Calgary on Wednesday.
"We showed lots of character. I'm very proud of our players," said Flames coach Bob Hartley, whose club is 3-1-1 on the road this year. "We had a good talk after the second period. I told them if we want to build some foundation to be a playoff team, it's games like this that we need to win."
Mike Cammalleri also scored for Calgary, while Joey MacDonald made 27 saves for his first win while making his first start and second appearance overall for the Flames since he was claimed off waivers from Detroit on Feb. 11.
"It's been a long time and it's been frustrating, ups and downs, good days, bad days," said MacDonald, who last won an NHL game on March 9, 2012. "But tonight 30 shots, I felt pretty good in there for not playing in a while."
Coming off an emotional 4-3 comeback triumph in Vancouver on Friday, the Stars were upset to have let this one slip away.
"It's very frustrating," said Smith, who scored for the second straight game. "With the big win in Vancouver, it's kind of not worth it anymore because with those two points that we should have had tonight, we let them go."
The result was particularly frustrating for the Stars because they reversed a disturbing trend that has plagued them this season by taking control of the contest with a strong second period, scoring three goals while outshooting Calgary 22-12, establishing a new season high for shots in a period. Over their first 15 contests, Dallas had been outscored 20-12 in middle frame.
"It's very disappointing, very disappointing that we didn't come out with two points here at home," Dallas coach Glen Gulutzan said. "We needed to be stronger in front of our net. You got to be battle-ready for 60 minutes. I think we just lost some battles."
With the Stars up 3-1 early in the final period, the Flames pulled even with two goals within a 45-second stretch that quieted the 17,340 in attendance.
First, Horak scored at 1:39 of the third, banging home a point-blank rebound after Bachman made a pad save on Jay Bouwmeester's wrist shot.
Stajan tied it at 2:24 after Lee Stempniak fed a backhand pass from behind the net out front, where Stajan drilled a one-timer past Bachman's glove.
"Our forechecking was much better, but more importantly we put pucks at the net with traffic and we found those loose pucks," Hartley said of the third period. "A great play by Stempniak on that short pass to Stajan. Tonight we had three huge goals in that third period."
Trailing 1-0 early in the second period, the Stars struck twice within 56 seconds to surge ahead 2-1.
Roussel tied it just 1:51 in, camping out in front to screen MacDonald and re-directing Cody Eakin's high, floating wrister over MacDonald's glove. The goal was originally credited to Eakin, but replays clearly showed the puck glancing off Roussel for his third of the year and second in the last two games.
Smith then recorded his second goal in as many games when he corralled his own rebound and lifted a backhander from the edge of the crease over a prone MacDonald at 2:47.
"I'm getting more comfortable every day," said Smith, a 21-year-old rookie who went scoreless in his first 12 games. "It was a tough start to the year, and I wanted to help the team a little bit more offensively. But everything's kind of happening for me out there right now."
The Stars made it 3-1 with 4:37 left in the second on Garbutt's third of the year. MacDonald made a pad save on Stephane Robidas' wrist shot from the left circle, but Garbutt pounced on the rebound and popped it over MacDonald's pad.
Garbutt, who fought Begin in the first period, now has three points (two goals, one assist) in four games since he sat out three in a row as a healthy scratch.
Calgary jumped on top 1-0 at 8:11 of the opening period when Cammalleri notched his fourth goal of the season -- all have come against Dallas. With the Flames still on a power play, and just 6 seconds after a 5-on-3 advantage expired, Cammalleri fired a wrist shot from a sharp angle to the right of the net and it slipped under Bachman's blocker and went in.
The loss for the Stars snapped a 79-game streak in which they hadn't lost in regulation after taking a lead into the third period, going 71-0-8 since falling to Nashville on Oct. 31, 2009. . Dallas D Trevor Daley left the contest after the second period with an upper body injury and did not return. He will be re-evaluated on Monday. ... Cammalleri continued his recent success against Dallas. He had a hat trick against the Stars in the Flames' 7-4 win Wednesday and now has 11 points (seven goals, four assists) in the last five meetings between the clubs. Overall, since missing three games with a lower body injury, he has collected four goals and two assists in the last three contests. ... Stars G Kari Lehtonen was placed on the injured list Sunday, retroactive to Friday, with a groin injury. He had to come out of the Stars' 4-3 win over Vancouver. He is not expected to be out more than the week he is required to spend on injured reserve.