Markstrom made 22 saves to reach an NHL career-high in shutouts, coming in nine starts this season.
"It says a lot more about the team and the way we're playing," Markstrom said. "It's really defensively sound and guys are blocking shots, and not only on the penalty kill and 5-on-5, but [the power play] has been great, it was great again today. Early, that was a difference-maker. We obviously got the goal from [Sean Monahan] and got a couple big kills that gave us the momentum to go the other way."
Monahan one-timed Tkachuk's cross-ice pass into the slot to put Calgary up 1-0 at 16:00 of the first period. The goal, on the power play, is Monahan's second in 11 games this season.
The Flames are 7-0-1 when scoring first this season.
Adam Fox, drafted by the Flames in the third round (No. 66) of the 2016 NHL Draft, scored with 1:43 remaining in the first, but Calgary successfully challenged Sammy Blais was offside before Fox entered the zone.
"It obviously would've been nice if that counted, but it was 1-0 at that point," Rangers forward Barclay Goodrow said. "One goal isn't going to deflate us when the lead is only one. Obviously it would've been great to have. We have to do a better job in responding after we get scored against."