Ryan Smith was whistled for roughing up Calgary goaltender Miikka Kiprusoff, putting the Flames on a power play, and Backlund made the Oilers pay with a goal 10:25 into the final frame for a 4-3 lead.
It came about 4 minutes after the Flames rallied from a 3-2 deficit with a Derek Smith goal. Calgary also came back from an early 2-0 hole to pull off their third win in four games.
Kiprusoff stopped 26-of-29 shots to earn the victory.
Lennart Petrell, Sam Gagner and Ryan Nugent-Hopkins scored for Edmonton, which lost for the fourth time in five games.
Nikolai Khabibulin made 27 saves for the Oilers.
Swim Week Miami Beach 2014 [PHOTOS]