Fiala and Filip Forsberg each had a goal and an assist, and Ryan Johansen, Craig Smith and Zac Rinaldo scored for Nashville (6-1-0), which won its fourth straight. The Predators, who haven't lost since Oct. 9, 3-0 to the Flames, have at least six wins through their first seven games in a season for the third time in their history (7-0-0 in 2005-06, 6-1-0 in 2015-16).
"We're really confident," Rinaldo said. "We have that swagger. We have attitude every single game. We bring speed every single game. But the thing about this group is we don't get comfortable. We know every game is going to be a hard-working game. We prepare for hard work every game. Confidence, but not comfortable."
Elias Lindholm and Matthew Tkachuk scored, and Mike Smith made 26 saves for the Flames (4-3-0), who had won two in a row.
"It was a tough game, 3-3 there, and they got a chance to score and that was the difference," Calgary captain Mark Giordano said.
Rinaldo's shot went past Smith's blocker on a 2-on-1 at 6:31 of the third period to put Nashville up 4-3. It was his first goal for the Predators since signing as a free agent July 2.
"The bench was pumped up," Laviolette said. "Just a great, great play. We ended up catching numbers going the other way. He made the right decision, made a great shot. It turned out to be the game-winner. It was a big goal."
Forsberg scored into an empty net with 32 seconds remaining to make it 5-3.
Johansen scored 51 seconds into the first period to put Nashville up 1-0. He has six points (two goals, four assists) during a four-game point streak.
"We're feeling good, for sure," Johansen said. "We understand it's a long season and there's a big process but we're just going to keep the peddle down and keep continuing to get better."