Gaudreau sent the puck low to Tkachuk, who stretched Price with a goal-mouth pass for Lindholm to tap in.
From the slot, Lindholm dished to Tkachuk beside the Habs web for the winger to sweep it over Price at 7:34.
The Flames play back-to-back road games Sunday and Monday facing the Dallas Stars and Minnesota Wild, respectively.
The Habs continue their trip through Western Canada on Saturday in Edmonton versus the Oilers and Monday against Winnipeg Jets.
Max Domi scored the overtime winner for the Montreal Canadiens in a 4-3 win over the Calgary Flames on Thursday.
Arturri Lehkonen fed Armia from the boards and the forward wristed the puck from the top of the faceoff circle bottom corner at 13:11.
Gallagher halved the deficit at 9:51. His shot along the goal-line from the boards squeezed by Rittich's blocker.
Calgary's power play generated a tic-tac-toe objective with 7 seconds left in the very first duration.