At 3:24 of the extra session, right winger Vladimir Tarasenko gave the Blues a 4-3 victory with his 10th goal of the season.
Tarasenko took a pass from Jori Lehtera and fired a wrist shot past Stars goalie Antti Niemi for 10th of the season and team-leading 23rd point.
The defender of the Stars Jamie Oleksiak scored two goals, including the one that created the tie with 50 seconds to make in the third period.
Robby Fabbri, Alex Pietrangelo and David Perron also scored for St. Louis, while Jamie Benn had the Stars' other goal.
Oleksiak scored twice, Benn recorded one goal and two assists, and Julius Honka chipped in two assists for the Stars, who have picked up points in eight of their past ten games (5-2-3) and are now 9-8-6 on the season.
The second goal from Pietrangelo marked the first time the Blues had held a two-goal lead in nine games, dating back to a 5-1 win over Colorado on November 6.
The 23-year-old Dallas blueliner, who is the older brother of Canadian Olympic swimmer Penny Oleksiak, entered the game with just two career goals to his name, but he matched that total on Wednesday night. "We leave a pretty good player wide open on the back side".
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Lee, who took over the reins after his father and Samsung patriarch was incapacitated following a May 2014 heart attack. The suggestion initially came from the hedge fund Elliott Management with the aim of increasing shareholder value.
For the second game in a row, the St. Louis Blues lost a late lead Monday night before coming back to win the game in overtime.
Pietrangelo poked in a loose puck under the Niemi's pad at 4:17 of the second period for a power-play goal. Charging the net, Pietrangelo pounced and knocked it in. "I'll take it. Everybody loves to score".
The goal impressed Dallas coach Lindy Ruff.
Bidding for his second goal of the night, Fabbri went on a breakaway less than two minutes after Pietrangelo's goal.
"The record indicates that you need a hard worker, you need a grind guy, a guy who can get inside and create a little more space and maybe wreak a little more havoc with the forecheck", Ruff said. "This was a game we had to have". The assist for Schwartz extended his streak to seven games (five goals, four assists).
Sean Monahan scored in the third for the Flames (10-13-2), who finished a six-game Eastern Conference road trip at 3-2-1. The Stars had a couple of power plays, but managed just one shot on goal and couldn't cut into the lead. Johns played in 16 games with Dallas earlier this season before being sent to the minors. But he appeared to struggle in adapting to the National Hockey League style early on, playing in only 19 games last season and has bounced in and out of the lineup this season. LW Alexander Steen and D Joel Edmundson (upper-body injuries) participated in the Blues' morning skate on Monday but were not ready to return to the lineup.