TJ Brodie scored at 2:09 of overtime, Johnny Gaudreau had two goals in regulation, and Calgary recovered after giving up a three-goal lead in the third period to beat the New York Rangers 5-4 on Saturday night for the Flames' ninth straight home victory.
Tanner Glass, Dan Boyle and Mats Zuccarello scored for the Rangers in the final 15 minutes of regulation to tie the score.
In the extra period, Brodie held the puck on a 2-on-1 rush and sent a shot inside the far goal post on Antti Raanta. It extended the defenseman's career-best point streak to six games (one goal, six assists).
Joe Colborne and Mason Raymond also scored Calgary (13-14-2), which opens a four-game road trip on Tuesday at Nashville.
J.T. Miller scored in the first period for the Rangers, who fell to 2-6-2 in their last 10 and finished a 0-2-1 road trip to western Canada.