Joe Colborne, Mark Giordano and Kevin Westgarth added markers for the Flames, winners in four of their last six.
Brian Boyle, Raphael Diaz and Brad Richards scored in a second-period burst for the Rangers, who were denied a sixth consecutive win in the first of four in a row on the road against Western Conference opponents.
Henrik Lundqvist stopped only 24-of-28 shots in defeat.
Notable deaths of 2014 [PHOTOS]
UPI Sports Results for September 19, 2014