Tim Stützle scored, and Kevin Mandolese made 34 saves for the Senators (33-29-4), who were coming off a 5-2 loss to the Vancouver Canucks on Saturday and are 1-3-0 during a season-long five-game road trip.
"There's parts of the game we need to clean up," Ottawa forward Austin Watson said. "That being said, you do have to address it and have a short memory because this time of year the next one matters as much as any of the rest. It's tough. It [stinks]. It's back-to-back games of outcomes that you don't want."
The Senators remained six points behind the New York Islanders, who have played two more games, for the second wild card into the playoffs from the Eastern Conference.
"We have a ton of belief in our group," Senators defenseman Travis Hamonic said. "We've been resilient all season. We've played through a ton of adversity. We've clawed our way back into the race and into the conversation when everyone kind of left us on the side of the road a couple months ago. That's something that we have an abundance of, I'd say, in our room. We know. The proof's in the pudding."
The Flames thought they took the lead at 8:18 of the first period when Tyler Toffoli scored on a deflection, but a video review determined Jakob Pelletier was offside prior to the goal.
Andersson did give Calgary a 1-0 lead at 12:09, scoring a short-handed goal blocker side after receiving a no-look backhand pass from Backlund in the slot.
"I was yelling before 'Backs' did the move on the [defenseman], and after he did the move, I didn't expect it," Andersson said. "But then it came on a silver platter so it was just put it in."