Jamie Benn scored for the Stars (36-28-10), who have won four straight games, seven of eight and nine of the past 11. The victory pulled Dallas within six points of the idle Winnipeg Jets, who hold the second wild card into the Stanley Cup Playoffs from the Western Conference, with eight games remaining.
"The thought has been win out really since I've come back from injury (on March 7)," Seguin said. "As long as I've been in the lineup that's been the message. I'm sure the guys were saying it before as well. We've been playing some good hockey, we've been finding ways to win and that's what it's all about.
"We were saying right before overtime, 'We're here for two points; we're not here for one.' It was a playoff-type game. They had momentum at times. We had momentum. I think both teams made some mistakes and both teams made some great plays. Obviously we're happy to walk away with both points."
"It's been exciting the last couple weeks," Lehtonen said. "We've been playing well and getting results and climbing a little bit, but we still have a little bit to go. It's a good thing we have some games left. I hope we can keep it up. It's going to be tight at the end. It sure makes it exciting."
The Flames (40-27-7) remained in third place in the Pacific Division and moved one point ahead of the Los Angeles Kings, who have a game in hand.
"Every point is going to count at the end," said Calgary defenseman Deryk Engelland, who scored his first two goals with the Flames in the loss. "It's a tight battle with a lot of teams, so we'll take every point we can get. We're trying for two every night, but if you get one, we'll take it and go."
"Honestly, I saw clips before the game of (Ramo) and I saw (Boston Bruins center Patrice) Bergeron (on March 5) go blocker on him," Seguin said. "My whole thing going down was I was going to shoot blocker. Once I saw that spot open, I just tried to have a quick release and it went in."
Seguin's shootout winner came after Engelland forced overtime, scoring his second of the game by sending a knuckler from the point that weaved through traffic and over Lehtonen's shoulder to tie the game 3-3 at 11:19.
"No matter if you score one or two or none, two points is what we need and coming down the stretch," Engelland said. "We'll take one but we needed that other one too."
The Stars came out strong in the first period.
Denied on his first attempt from in close, Benn kicked his own rebound up to his stick and tried to tuck a shot by the pad of Ramo, but the puck popped up and rested on Ramo's leg up against the goal line on Dallas' first scoring chance 6:30 into the game.
With Markus Granlund serving a double-minor for high sticking, the Stars had five shots on Ramo, including a sequence that featured a blocker save off Benn followed by a kick save against Seguin, as well as a slap shot from Alex Goligoski that was also denied by Ramo's pad midway through the period.
After Hemsky put the Stars up 1-0 47 seconds into the second, Benn extended the lead 10 minutes later.
On the power play with Colborne in the penalty box for holding, Jason Spezza toe-dragged the puck around a sliding Kris Russell before feeding Benn for a tap-in for his 27th goal of the season at 10:47 to give Dallas a 2-0 lead.
But Gaudreau converted on a tic-tac-toe play set up by Jiri Hudler and Monahan at 12:44 and Engelland, with a seeing-eye shot through a screen, scored his first goal since March 7, 2014, to tie the game at 13:49.
Skating 4-on-4, Shawn Horcoff stripped Bouma at the Stars blue line before hauling the puck up ice on a 2-on-1. Horcoff slid a pass across to Hemsky, who scored on a wraparound to make it 3-2. It was his 11th of the season.