Elias Lindholm added a goal and two assists, defensemen Rasmus Andersson and MacKenzie Weegar also scored, and Jacob Markstrom made 34 saves.
Mark Scheifele, Kyle Connor and Alex Iafallo scored for Winnipeg, with Connor Hellebuyck stopping 17 shots.
Winnipeg outshot Calgary 28-14 after two periods, but trailed 3-2.
Scheifele tied it with 5:42 left, and Lindholm put the Flames back in front with 1:32 to go when he was fed by Mangiapane from behind the net. Mangiapane added an empty-netter.
Jets: Host Florida on Saturday.
Flames: At Pittsburgh on Saturday night.
AP NHL: https://apnews.com/hub/nhl
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