Kyle Connor scored a power-play goal and had two assists, and Connor Hellebuyck made 23 saves for the Jets.
Laine had an assist on Connor's goal.
"Three points, it's not always going to tell the whole story," Laine said. "Hopefully, I can just build off that game. There's a lot of things we need to work on, and the three points are not going to tell the true story of the game. Obviously, it's a good start. You've got to produce, so that was good, and it was two big points for us."
Matthew Tkachuk, Johnny Gaudreau and Elias Lindholm scored for Calgary, and Jacob Markstrom made 30 saves in his Flames debut.
"I think overall [Markstrom] has been looking really good and he's been excited to get going and get the first game in," Lindholm said. "He saved us at least one point tonight, so all credit to him. I think everyone wants to win in there, and after such a good first (period), I think we let everyone down, and we didn't come out in the second and third and play the way we wanted, so that's got to change to the next game."