The clubs played a frantic final few minutes of regulation when the Rangers were given power plays 40 seconds apart after Mike Cammalleri was sent off for roughing, and Ramo was called for delay of game when he whacked a rebound out of play.
That advantage was short-circuited right when Cammalleri's penalty ended when Kreider was given four minutes for high-sticking Chris Butler.
The Rangers got it to overtime, with Calgary still having 2:04 left on its power play.
"Thought we'd get it done in overtime, but we couldn't execute on the power play," Flames captain Mark Giordano said. "We're not happy with the point. It should have been two.
"If you get a power play in overtime, you should win."
The Flames had won their first two since general manager Jay Feaster and assistant GM John Weisbrod were fired Thursday.
New York tied it at 2 at 7:29 of the second on Hagelin's sixth goal. Hagelin got to a rebound, swung around the net and stuffed a shot inside the right post.
The Rangers again had a rough first period, but it was actually a better start than in their previous game — holding the Flames to two goals. The Rangers trailed Columbus 3-0 in the opening frame on Thursday, and Lundqvist was chased from the net 11:10 into the 3-2 loss.
Calgary got the quick jump when Backlund scored at 7:28, just five seconds into a power play after Kreider was sent off for interference. Backlund won a faceoff in the left circle and moved into the slot, where he deftly tipped in Hudler's shot for his fourth goal.
The Flames made it 2-0 with 5:00 left in the period. Hudler weaved his way in close and made a short backhanded pass to Glencross, who used his own backhand to beat Lundqvist for his sixth goal.
The announcement of Glencross' goal was only halfway finished when Stepan brought a roar from the crowd with his sixth of the season 25 seconds later. It was Stepan's first goal in 11 games.
NOTES: Stepan earned his 100th NHL assist on Kreider's goal. ... Giordano played in his 400th NHL game. ... Calgary's previous four games were decided by 2-1 scores. ... The Rangers used seven defensemen and only 11 forwards in their lineup.