Nazem Kadri had a goal and an assist, Kevin Bahl and Yegor Sharangovich also scored, and Mikael Backlund had two assists for the Flames (2-7-1), who had been outscored 31-12 during the streak (0-7-1). Dustin Wolf made 30 saves.
Noah Laba scored his first NHL goal for the Rangers (3-5-2), who have lost three in a row (0-2-1) and six of their past seven (1-4-2). Igor Shesterkin made 25 saves.
Kadri gave the Flames a 1-0 lead at 1:42 of the first period. He lost control of the puck while trying to make a move around Mika Zibanejad in the right circle, but it went right to Jonathan Huberdeau, who dropped a pass right back to Kadri for a snap shot from the right circle.
Bahl made it 2-0 at 9:21 with a wrist shot from the high slot that went glove side on Shesterkin, who was screened by teammate Alexis Lafreniere.
Laba, who was playing in his 10th NHL game, cut it to 2-1 just 10 seconds later. He took a pass at the blue line and skated hard to the net down the left wing before lifting a shot over Wolf’s left pad.
Wolf responded by stopping a pair of breakaways in the second period to preserve the one-goal lead. He first made a blocker save on Laba at 1:41 before doing the splits in order to turn aside a shot by Mika Zibanejad with his left pad at 9:48.
Sharangovich then scored his first goal of the season to put the Flames up 3-1 at 12:28 of the second. Connor Zary made a move around Braden Schneider and skated down the right wing before sending a backhand pass to Sharangovich, whose one-timer from the low slot hit off Shesterkin’s glove before trickling into the net.
Coleman extended the lead to 4-1 at 6:42 of the third period, tapping in a return pass from Backlund on a short-handed 2-on-1 rush.
Coleman scored again at 14:27 when his shot deflected off Lafreniere and fluttered past Shesterkin to make it 5-1.