Gustafsson extended it to 3-1 at 16:53 on a 4-on-4 when he poked a loose puck over the goal line after Chytil’s initial shot trickled under the arm of Markstrom.
"Just a tough second period," Flames captain Mikael Backlund said. "We came out, played well in the first, especially the first half of the first, and then we let them come into the game and they took over and they carried it a little bit in the second."
Shesterkin made a sprawling pad save on Jonathan Huberdeau at 9:31 of the third period on a backdoor setup from Elias Lindholm.
Shesterkin also stopped Nazem Kadri's wrist shot at 17:58 to help preserve the win for New York.
"The only guys that are going to get us out of this rut are the 20 guys that are in this room," Calgary defenseman MacKenzie Weegar said. "We've got to work hard. I've said this all along. We've got the compete, we've got the effort in here, we've got the guys. We're just in a bit of a slump; it came early. I believe we can get out of it. But it's going to take hard work and we've got to put an end to it ASAP."
Flames forward Adam Ruzicka sustained an apparent upper-body injury at 18:32 of the first period on a hit by Rangers forward Jimmy Vesey and did not return.
NOTES: Kreider has five goals in six games to start the season. He needs three more to tie Andy Bathgate for fourth-most in Rangers history. ... Panarin has eight points (three goals, five assists) during his 6-game point streak. ... Coleman's goal was his 200th point in the NHL. He is the third Texas-born NHL player to eclipse 200 points, joining Brian Leetch (1,028) and Seth Jones (377). ... Chytil has five assists in his past two games. ... There was no update on Ruzicka postgame.