Forward Mike Santorelli, who was acquired from the Canucks in the offseason from the Winnipeg Jets, scored twice including an overtime marker with 1:43 left in the extra period.
The Flames meanwhile got goals from David Jones, Mark Giordano, Mikael Backlund and Sean Monahan. Jones scored with 19 seconds left in regulation to preserve a Flames point. Giordano's goal was his first as a Flames captain.
Jones (a goal and an assist) and Jiri Hudler led the Flames with two points each.
Goaltender Joey MacDonald made his second consecutive start after he defeated the Columbus Blue Jackets 4-3 on Friday.
Even though Flames rookie Monahan scored, he was a team low -3. From a statistical perspective, there are obviously improvements that are needed in that area of his game.
The Flames will next play the Montreal Canadiens on Wednesday at the Scotiabank Saddledome. Note the start time is 6:00 p.m. to accommodate TSN.