Tanguay, Calgary’s first shooter, skated to the left and buried a wrister past Kari Lehtonen.
Miikka Kiprusoff then stopped Brad Richards’ wrister with a glove save and Mike Ribeiro lost the puck on Dallas’ last chance.
Anton Babchuk scored the other goal for the Flames, who had dropped their previous three games. Kiprusoff stopped 14 shots through regulation and overtime.
Ribeiro had a goal and an assist and Brenden Morrow scored the other goal for the Stars, who had a three-game winning streak stopped. Lehtonen made 30 saves in the defeat.
Calgary was trailing by a goal late in the game, but tied it up with the extra attacker as Tanguay found himself alone with the puck and from the slot he snapped a wrister into the left corner of the net with 1:21 to play.
The Flames took a 1-0 lead with 8:57 left in the first on the power play when Babchuk slapped a shot from the top of the left circle through a screen and past Lehtonen for his fifth goal of the season.
The Stars, though, answered with a power-play goal of their own later in the first as Ribeiro’s one-timer from the right circle blew past Kiprusoff with 2:47 left in the stanza.
After a scoreless second period which saw Lehtonen make 10 saves and Kiprusoff face just two, the Stars took a 2-1 lead 2:41 into the third.
A slap pass from Ribeiro at the right circle to the slot saw Morrow whack it in on his second attempt for his 13th goal of the season.
Dallas hosts Phoenix on Sunday…Calgary returns home to face Buffalo on Monday…The Stars took three of four from the Flames last season…Dallas went 1-for-3 on the power play while Calgary was 1-for-4.