David Rittich made 31 saves for Calgary, which plays here again Monday.
Drake Batherson had a goal and an assist for Ottawa, which had its three-game winning streak end. Matt Murray allowed six goals on 33 shots and was replaced by Joey Daccord, who made five saves in his season debut.
"Our game is forechecking, physical, play off the cycle, and we did that in the third period, but we've got to come out ready when the game starts," Senators coach D.J. Smith said.
Juuso Valimaki one-timed a pass from Johnny Gaudreau to give the Flames a 1-0 lead at 4:00 of the first period. It was Valimaki's first NHL goal since Oct. 17, 2018; he missed last season with a knee injury.
"I'm not going to lie, that felt pretty good," Valimaki said.
Backlund's wrist shot on the rush went off the right post to make it 2-0 at 4:37. Lindholm's quick shot along the ice fooled Murray to make it 3-0 at 11:05.
"Right from the first 10 minutes, I thought we took charge of the game," Backlund said. "We played a solid game throughout the day."