Mikael Backlund scored five seconds into Chris Kreider's interference penalty in the first period.
Curtis Glencross notched his sixth goal of the year at the 15:00 mark of the first period after Jiri Hudler undressed a Ranger with some filthy stickwork in tight. He dished it off to a wide-open Glencross for the Flames second goal.
With his third period marker, rookie Sean Monahan has hit the 10-goal mark this season. Curtis Glencross and Jiri Hudler assisted on the tally.
Jiri Hudler has now hit the 30-point plateau thanks to his two assists.
Lance Bouma blocked four shots in his 8:34 of ice time. The rugged winger's four blocks all came in the opening period, with two being key on a penalty killing sequence.
The Flames played in their third straight game with overtime. It was their fourth shootout of the year.
In his third consecutive start, Karri Ramo made 29 saves.