Blake Coleman scored his first goal of the season, and Jacob Markstrom made 28 saves for the Flames (5-4-0), who have lost three straight and are 3-4-0 on a season-long eight-game homestand.
"It's unacceptable, the whole thing," Coleman said. "Regardless of what the games before, the outcomes were. It's a home game, it's a game we needed to win. It's a game you want to have right from the get-go, and we didn't have it. Unacceptable is the best way to describe it."
Mark Jankowski put Nashville up 1-0 at 19:31 of the first period, scoring on a rebound after Markstrom kicked Michael McCarron's sharp-angled shot into the slot.
Jankowksi, who was originally selected by the Flames in the first round (No. 21) of the 2012 NHL Draft and played 208 games with Calgary, made his season debut after being recalled from Milwaukee of the American Hockey League earlier Thursday.
"It's funny how the world works like that," Jankowski said. "There's so many good memories here. This is where my career started. So many great memories. So many great friends I still have on the other side over there. It's really special."