Tanguay's score in the opening round of the shootout was answered by Minnesota's Patrick O'Sullivan to start the third. Bourque then put a wrist shot between the pads of Niklas Backstrom to give the Flames the win.
Calgary defeated Minnesota for the second time in five games and handed the Wild their fourth straight loss.
It was a 1-1 contest heading into the third period, but Tanguay gave Calgary the lead 4:29 into the stanza with his eighth goal of the season. Martin Havlat tied it on a backhander with 7:21 to play in regulation.
Henrik Karlsson was given the third start of his rookie season in place of Miikka Kiprusoff and made 20 saves to get his second win. Kiprusoff gave up seven goals on Wednesday against Vancouver.
Backstrom stopped 30 shots in the loss.