Flames goaltender Karri Ramo made 23 saves for Calgary, who recorded his first career National Hockey League shutout.
Backlund's game winning goal on the power play with 4:34 left in the second period was his second goal in two games as he scored Calgary's lone goal Saturday against Pittsburgh.
Monahan meanwhile found himself wide open a three-on-two rush for a key insurance marker.
With the win, the Flames improve to 16-24-6 and will next play in Nashville on Tuesday. The Flames also have an amazing record this season of 5-0 on Monday nights. They have previously beaten the Los Angeles Kings, Winnipeg Jets, St. Louis Blues and Colorado Avalanche this season on Monday.