"I think you have great goalies and you have elite goalies and why we're saying Kari's elite is because his level of play is rising in important games," Dallas coach Glen Gulutzan said. "They threw a lot of bodies at him and there's going to be more, but he's a big guy, he fights through it.
"He looked like he was in the zone, catching pucks with guys in front of him, giving our team a lot of confidence. You see a different level coming out of Kari right now."
Michael Ryder also scored for the Stars, who improved to 87 points and are in the middle of a six-team scramble along with the Flames (83 points) for one of the final two playoff spots in the West.
After giving up two goals in the game's first 8 minutes, the Flames raised their competitive level and narrowed the deficit to one on Mike Cammalleri's first-period goal.
Calgary kept the momentum with a 14-6 edge in shots in a scoreless second period, but Lehtonen didn't crack.
"We played a pretty darned good hockey game ... didn't give them hardly any shots at all," Flames coach Brent Sutter said. "Their goaltender definitely was first star tonight."
The Stars moved into the Pacific Division lead with a 10-0-1 run, but they'd lost three of their previous four to tumble out of the top spot in the division and hurt their playoff chances.
Brenden Morrow tapped in an empty-netter at 18:32 of the third period to clinch the win for Dallas.
Miikka Kiprusoff stopped 16 shots for the Flames, who lost their previous three games in overtime or shootouts.
Dallas wrapped up a 2-2 homestand and begins a four-game trip Monday night in Calgary, the next game for both teams.
Calgary, which is 5-2-4 in its past 11 games, completed an 0-1-2 road trip.
Time is running out for the Flames, who have six games left.
"We realize out of six games, we most likely have to win them all," captain Jarome Iginla said. "Our chances are slim. We most likely have to run the table. But we won't give up."
Benn got his team off to a fast start at 1:37 of the first period, taking a pass from Adam Burish, skating from behind the net and stuffing a shot past Kiprusoff on Dallas' first shot of the game.
Lehtonen got a break at 3:03 of the opening period when a shot by Calgary's Blake Comeau banged off the right post. Otherwise, he was just about perfect.
"That was fun," said Lehtonen, who allowed nine goals in his previous three starts. "I didn't feel like I've been at my best the last three games, so it was nice to be able to help out and get some good saves. It's great to get two points. These are some important games. We just have to keep going."
Ryder made it 2-0 at 7:17 of the first, firing his career-best 33rd goal by Kiprusoff from the right circle.
The Flames pulled within one when Cammalleri notched his 16th from the right circle at 12:27 of the first period.
Cammalleri had missed the previous nine games with an upper-body injury.
Calgary had been dominating play before Benn scored on a one-timer from the slot off Steve Ott's pass to give Dallas a two-goal cushion at 16:27 of the final period, Benn's 24th of the season.
"They were making a pretty good push there, but our goalie stood strong and (Ott) made a pretty good pass there and I kind of finished them off," Benn said.
The Flames continue to struggle on offense, having managed six goals in their past five games.
"We had lots of shots, lots of great scoring chances," said Iginla, who doesn't have a point in his last five games. "Unfortunately, in these last five games they haven't gone in for us. It definitely stings. It's a tough loss for us."
The Stars paid tribute to former D Karlis Skrastins prior to the game. Skrastins was a member of the Lokomotiv Yaroslavl team when the Latvian native died in a plane crash in Russia last September en route to a Kontinental League game in Minsk. His widow, Zane, and three daughters participated in the ceremony. The Stars have been wearing No. 37 patches on their uniforms this season in honor of Skrastins, who played two full seasons in Dallas. ... D Mark Fistric (abdominal strain) was out for Dallas. ... The Flames were without C Mikael Backlund (shoulder), D T.J. Brodie (upper body) and D Cory Sarich (upper body). ... Dallas has seven games remaining, five on the road.