Calgary pulled out the win when Backlund scored on the rebound of a Sean Monahan shot in extra time.
TJ Galiardi notched a goal and an assist, and Dennis Wideman also scored for the Flames, who wrapped up a 5-0-0 homestand.
Reto Berra earned the win after taking over for the injured Karri Ramo late in the first period, stopping 14-of-17 shots.
Heatley added an assist and Matt Cooke also scored for the Wild, who went 1-1-2 on a four-game road swing.
Darcy Kuemper made 28 saves.
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