Gaudreau made it 2-0 at 15:20, and Valimaki, 20, scored his first NHL goal 48 seconds later to give Calgary a 3-0 lead. It was Valimaki's sixth NHL game.
"I didn't know [the goal was mine]," Valimaki said. "It was kind of an awkward moment because I wasn't sure if it was mine or [Sam Bennett]'s. That's why I didn't [celebrate] too hard."
David Pastrnak scored at 17:32, but Peters challenged that Bergeron was offside and the goal was overturned following a video review.
Bergeron scored 2:40 into the second period to make it 3-1, but Frolik scored on a setup from Backlund 52 seconds later to put Calgary up 4-1.
"I didn't have the start I was looking for but it's a long season," said Frolik, who had one point (goal) in four games. "There's a lot of games in front of us. I just try to work hard in practice and try to get better every day and hopefully it's going to turn around, and I think tonight was a good start. Hopefully I can keep going."
Marchand scored on a pass from Bergeron to cut the lead to 4-2 at 13:45. Bergeron and Marchand each have five-game point streaks; Bergeron has 13 points (six goals, seven assists) and Marchand has 11 points (two goals, nine assists).